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  Subjects -> PHYSICS (Total: 736 journals)
    - ELECTRICITY (2 journals)
    - MECHANICS (5 journals)
    - NUCLEAR PHYSICS (28 journals)
    - OPTICS (53 journals)
    - PHYSICS (623 journals)
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PHYSICS (623 journals)                  1 2 3 4 5 6 7 | Last

Acoustical Physics     Hybrid Journal   (8 followers)
Acoustics Today     Hybrid Journal   (2 followers)
Acta Acustica united with Acustica     Full-text available via subscription   (7 followers)
Acta Mechanica     Hybrid Journal   (15 followers)
Acta Mechanica Sinica     Hybrid Journal   (4 followers)
Acta Physica Slovaca     Open Access   (3 followers)
Advanced Composite Materials     Hybrid Journal   (10 followers)
Advanced Electromagnetics     Open Access   (9 followers)
Advanced Functional Materials     Hybrid Journal   (29 followers)
Advanced Materials     Hybrid Journal   (205 followers)
Advances in Acoustics and Vibration     Open Access   (16 followers)
Advances In Atomic, Molecular, and Optical Physics     Full-text available via subscription   (4 followers)
Advances in Condensed Matter Physics     Open Access   (6 followers)
Advances in Exploration Geophysics     Full-text available via subscription   (3 followers)
Advances in Geophysics     Full-text available via subscription   (4 followers)
Advances in High Energy Physics     Open Access   (12 followers)
Advances in Imaging and Electron Physics     Full-text available via subscription   (1 follower)
Advances in Materials Physics and Chemistry     Open Access   (7 followers)
Advances in Natural Sciences: Nanoscience and Nanotechnology     Open Access   (13 followers)
Advances in Nonlinear Optics     Open Access   (2 followers)
Advances in OptoElectronics     Open Access   (2 followers)
Advances In Physics     Hybrid Journal   (6 followers)
Advances in Physics Theories and Applications     Open Access   (4 followers)
Advances in Remote Sensing     Open Access   (7 followers)
Advances in Synchrotron Radiation     Hybrid Journal   (1 follower)
AIP Advances     Open Access   (4 followers)
American Journal of Applied Sciences     Open Access   (27 followers)
American Journal of Condensed Matter Physics     Open Access   (2 followers)
Analysis and Mathematical Physics     Hybrid Journal   (2 followers)
Annalen der Physik     Hybrid Journal   (2 followers)
Annales Geophysicae (ANGEO)     Open Access   (3 followers)
Annales Henri PoincarĂ©     Hybrid Journal   (2 followers)
Annales UMCS, Physica     Open Access  
Annals of Nuclear Medicine     Hybrid Journal   (2 followers)
Annals of Physics     Hybrid Journal   (2 followers)
Annual Reports on NMR Spectroscopy     Full-text available via subscription   (1 follower)
Annual Review of Analytical Chemistry     Full-text available via subscription   (8 followers)
Annual Review of Condensed Matter Physics     Full-text available via subscription   (1 follower)
Annual Review of Fluid Mechanics     Full-text available via subscription   (11 followers)
Annual Review of Materials Research     Full-text available via subscription   (4 followers)
Annual Review of Nuclear and Particle Science     Full-text available via subscription   (1 follower)
APL : Organic Electronics and Photonics     Hybrid Journal   (1 follower)
APL Materials     Open Access   (1 follower)
Applied Acoustics     Hybrid Journal   (3 followers)
Applied Composite Materials     Hybrid Journal   (8 followers)
Applied Mathematics and Mechanics     Hybrid Journal   (2 followers)
Applied Physics A     Hybrid Journal   (9 followers)
Applied Physics Frontier     Open Access  
Applied Physics Letters     Hybrid Journal   (22 followers)
Applied Physics Research     Open Access   (5 followers)
Applied Physics Reviews     Hybrid Journal   (7 followers)
Applied Radiation and Isotopes     Hybrid Journal   (5 followers)
Applied Remote Sensing Journal     Open Access   (6 followers)
Applied Spectroscopy     Full-text available via subscription   (11 followers)
Applied Spectroscopy Reviews     Hybrid Journal   (2 followers)
Applied Thermal Engineering     Hybrid Journal   (3 followers)
Archive for Rational Mechanics and Analysis     Hybrid Journal   (3 followers)
Astronomy & Geophysics     Hybrid Journal   (1 follower)
Astrophysical Journal Letters     Full-text available via subscription   (2 followers)
Astrophysical Journal Supplement Series     Full-text available via subscription   (2 followers)
Atmospheric and Oceanic Optics     Hybrid Journal  
Atomic Data and Nuclear Data Tables     Hybrid Journal  
Atoms     Open Access  
Attention, Perception & Psychophysics     Full-text available via subscription   (4 followers)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (5 followers)
Axioms     Open Access  
Bangladesh Journal of Medical Physics     Open Access  
Bauphysik     Hybrid Journal   (1 follower)
Biomaterials     Hybrid Journal   (22 followers)
Biomedical Engineering, IEEE Reviews in     Full-text available via subscription   (14 followers)
Biomedical Engineering, IEEE Transactions on     Hybrid Journal   (11 followers)
Biomedical Imaging and Intervention Journal     Open Access   (4 followers)
Biophysical Reviews     Hybrid Journal  
Biophysical Reviews and Letters     Hybrid Journal   (3 followers)
BMC Biophysics     Open Access   (7 followers)
BMC Nuclear Medicine     Open Access   (4 followers)
Brazilian Journal of Physics     Hybrid Journal  
Broadcasting, IEEE Transactions on     Hybrid Journal   (5 followers)
Building Acoustics     Full-text available via subscription   (1 follower)
Bulletin of Materials Science     Open Access   (34 followers)
Bulletin of the Atomic Scientists     Full-text available via subscription   (3 followers)
Bulletin of the Lebedev Physics Institute     Hybrid Journal   (2 followers)
Bulletin of the Russian Academy of Sciences: Physics     Hybrid Journal   (1 follower)
Caderno Brasileiro de Ensino de FĂ­sica     Open Access  
Canadian Journal of Physics     Full-text available via subscription   (2 followers)
Cells     Open Access  
Central European Journal of Physics     Hybrid Journal   (2 followers)
Chinese Journal of Astronomy and Astrophysics     Full-text available via subscription  
Chinese Journal of Chemical Physics     Hybrid Journal   (1 follower)
Chinese Physics B     Full-text available via subscription  
Chinese Physics C     Full-text available via subscription  
Chinese Physics Letters     Full-text available via subscription  
Cohesion and Structure     Full-text available via subscription   (1 follower)
Colloid Journal     Hybrid Journal   (1 follower)
Communications in Mathematical Physics     Hybrid Journal   (3 followers)
Communications in Numerical Methods in Engineering     Hybrid Journal   (4 followers)
Communications in Theoretical Physics     Full-text available via subscription   (2 followers)
Composites Part A : Applied Science and Manufacturing     Hybrid Journal   (23 followers)
Composites Part B : Engineering     Hybrid Journal   (21 followers)
Computational Materials Science     Hybrid Journal   (15 followers)

        1 2 3 4 5 6 7 | Last

Archive for Rational Mechanics and Analysis    [5 followers]  Follow    
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
     ISSN (Print) 1432-0673 - ISSN (Online) 0003-9527
     Published by Springer-Verlag Homepage  [2187 journals]   [SJR: 3.43]   [H-I: 51]
  • Global Classical Solutions for Partially Dissipative Hyperbolic System of
           Balance Laws
    • Abstract: Abstract The basic existence theory of Kato and Majda enables us to obtain local-in-time classical solutions to generally quasilinear hyperbolic systems in the framework of Sobolev spaces (in x) with higher regularity. However, it remains a challenging open problem whether classical solutions still preserve well-posedness in the case of critical regularity. This paper is concerned with partially dissipative hyperbolic system of balance laws. Under the entropy dissipative assumption, we establish the local well-posedness and blow-up criterion of classical solutions in the framework of Besov spaces with critical regularity with the aid of the standard iteration argument and Friedrichs’ regularization method. Then we explore the theory of function spaces and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin–Lerner spaces (mixed space-time Besov spaces). This fact allows us to capture the dissipation rates generated from the partial dissipative source term and further obtain the global well-posedness and stability by assuming at all times the Shizuta–Kawashima algebraic condition. As a direct application, the corresponding well-posedness and stability of classical solutions to the compressible Euler equations with damping are also obtained.
      PubDate: 2014-02-01
       
  • A Parabolic Free Boundary Problem Modeling Electrostatic MEMS
    • Abstract: Abstract The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right-hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time, while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified.
      PubDate: 2014-02-01
       
  • Linear Stability Analysis of a Hot Plasma in a Solid Torus
    • Abstract: Abstract This paper is a first step toward understanding the effect of toroidal geometry on the rigorous stability theory of plasmas. We consider a collisionless plasma inside a torus, modeled by the relativistic Vlasov–Maxwell system. The surface of the torus is perfectly conducting and it reflects the particles specularly. We provide sharp criteria for the stability of equilibria under the assumption that the particle distributions and the electromagnetic fields depend only on the cross-sectional variables of the torus.
      PubDate: 2014-02-01
       
  • Monotonicity Formula and Regularity for General Free Discontinuity
           Problems
    • Abstract: Abstract We give a general monotonicity formula for local minimizers of free discontinuity problems which have a critical deviation from minimality, of order d − 1. This result allows us to prove partial regularity results (that is closure and density estimates for the jump set) for a large class of free discontinuity problems involving general energies associated to the jump set, as for example free boundary problems with Robin conditions. In particular, we give a short proof to the De Giorgi–Carriero–Leaci result for the Mumford–Shah functional.
      PubDate: 2014-02-01
       
  • Real Solutions to the Nonlinear Helmholtz Equation with Local Nonlinearity
    • Abstract: Abstract In this paper, we study real solutions of the nonlinear Helmholtz equation $$- \Delta u - k^2 u = f(x,u),\quad x\in \mathbb{R}^N$$ satisfying the asymptotic conditions $$u(x)=O\left( x ^{\frac{1-N}{2}}\right) \quad {\rm and} \quad \frac{\partial^2 u}{\partial r^2}(x)+k^2u(x)=o\left( x ^{\frac{1-N}{2}}\right) \quad {\rm as}\, r= x \to\infty.$$ We develop the variational framework to prove the existence of nontrivial solutions for compactly supported nonlinearities without any symmetry assumptions. In addition, we consider the radial case in which, for a larger class of nonlinearities, infinitely many solutions are shown to exist. Our results give rise to the existence of standing wave solutions of corresponding nonlinear Klein–Gordon equations with arbitrarily large frequency.
      PubDate: 2014-02-01
       
  • Orbital Stability of Periodic Peakons to a Generalized        class="a-plus-plus">μ-Camassa–Holm
           Equation
    • Abstract: Abstract In this paper, we study the orbital stability of the periodic peaked solitons of the generalized μ-Camassa–Holm equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Camassa–Holm equation and the modified Camassa–Holm equation. It is also integrable with the Lax-pair and bi-Hamiltonian structure and admits the single peakons and multi-peakons. By constructing an inequality related to the maximum and minimum of solutions with the conservation laws, we prove that, even in the case that the Camassa–Holm energy counteracts in part the modified Camassa–Holm energy, the shapes of periodic peakons are still orbitally stable under small perturbations in the energy space.
      PubDate: 2014-02-01
       
  • Stabilization in a two-dimensional chemotaxis-Navier–Stokes system
    • Abstract: Abstract This paper deals with an initial-boundary value problem for the system $$\left\{ \begin{array}{llll} n_t + u\cdot\nabla n &=& \Delta n -\nabla \cdot (n\chi(c)\nabla c), \quad\quad & x\in\Omega, \, t > 0,\\ c_t + u\cdot\nabla c &=& \Delta c-nf(c), \quad\quad & x\in\Omega, \, t > 0,\\ u_t + \kappa (u\cdot \nabla) u &=& \Delta u + \nabla P + n \nabla\phi, \qquad & x\in\Omega, \, t > 0,\\ \nabla \cdot u &=& 0, \qquad & x\in\Omega, \, t > 0,\end{array} \right.$$ which has been proposed as a model for the spatio-temporal evolution of populations of swimming aerobic bacteria. It is known that in bounded convex domains ${\Omega \subset \mathbb{R}^2}$ and under appropriate assumptions on the parameter functions χ, f and ϕ, for each ${\kappa\in\mathbb{R}}$ and all sufficiently smooth initial data this problem possesses a unique global-in-time classical solution. The present work asserts that this solution stabilizes to the spatially uniform equilibrium ${(\overline{n_0},0,0)}$ , where ${\overline{n_0}:=\frac{1}{ \Omega } \int_\Omega n(x,0)\,{\rm d}x}$ , in the sense that as t→∞, $$n(\cdot,t) \to \overline{n_0}, \qquad c(\cdot,t) \to 0 \qquad \text{and}\qquad u(\cdot,t) \to 0$$ hold with respect to the norm in ${L^\infty(\Omega)}$ .
      PubDate: 2014-02-01
       
  • A Comparison Principle for Singular Diffusion Equations with Spatially
           Inhomogeneous Driving Force for Graphs
    • Abstract: Abstract We introduce the notions of viscosity super- and subsolutions suitable for singular diffusion equations of non-divergence type with a general spatially inhomogeneous driving term. In particular, the viscosity super- and subsolutions support facets and allow a possible facet bending. We prove a comparison principle by a modified doubling variables technique. Finally, we present examples of viscosity solutions. Our results apply to a general crystalline curvature flow with a spatially inhomogeneous driving term for a graph-like curve.
      PubDate: 2014-02-01
       
  • KdV Limit of the Euler–Poisson System
    • Abstract: Abstract Consider the scaling ${\varepsilon^{1/2}(x-Vt) \to x, \varepsilon^{3/2}t \to t}$ in the Euler–Poisson system for ion-acoustic waves (1). We establish that as ${\varepsilon \to 0}$ , the solutions to such Euler–Poisson systems converge globally in time to the solutions of the Korteweg–de Vries equation.
      PubDate: 2014-02-01
       
  • Local Minimizers and the Schmid Law in Corner-Shaped Domains
    • Abstract: Abstract This paper focuses on the mathematical analysis of biaxial loading experiments in martensite, more particularly on how hysteresis relates to metastability. These experiments were carried out by Chu and James and their mathematical treatment was initiated by Ball, Chu and James. Experimentally it is observed that a homogeneous deformation y 1 is the stable state for “small” loads while y 2 is stable for “large” loads. A model was proposed by Ball, Chu and James which, for a certain intermediate range of loads, predicts crucially that y 1 remains metastable (that is, a local—as opposed to global—minimiser of the energy). This result explains convincingly the hysteresis that is observed experimentally. It is easy to get an upper bound on the load at which metastability finishes. However, it was also noticed that this bound (the Schmid Law) may not be sharp, though this required some geometric conditions on the sample. In this research, we rigorously justify the Ball–Chu–James model by means of De Giorgi’s Γ-convergence, establish some properties of local minimisers of the (limiting) energy and prove the metastability result mentioned above. An important part of the paper is then devoted to establishing which geometric conditions are necessary and sufficient for the counter-example to the Schmid Law to apply, namely, the presence of sharp corners in the sample.
      PubDate: 2014-02-01
       
  • Global Boundedness of the Gradient for a Class of Nonlinear Elliptic
           Systems
    • Abstract: Abstract Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly non-polynomial type are allowed, and minimal regularity on the data and on the boundary of the domain is assumed. The case of arbitrary bounded convex domains is also included.
      PubDate: 2014-01-23
       
  • A Priori Estimates for Free Boundary Problem of Incompressible Inviscid
           Magnetohydrodynamic Flows
    • Abstract: Abstract In the present paper, we prove the a priori estimates of Sobolev norms for a free boundary problem of the incompressible inviscid magnetohydrodynamics equations in all physical spatial dimensions n = 2 and 3 by adopting a geometrical point of view used in Christodoulou and Lindblad (Commun Pure Appl Math 53:1536–1602, 2000), and estimating quantities such as the second fundamental form and the velocity of the free surface. We identify the well-posedness condition that the outer normal derivative of the total pressure including the fluid and magnetic pressures is negative on the free boundary, which is similar to the physical condition (Taylor sign condition) for the incompressible Euler equations of fluids.
      PubDate: 2014-01-15
       
  • The Hele–Shaw Asymptotics for Mechanical Models of Tumor Growth
    • Abstract: Abstract Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. Our first goal here is to formulate a free boundary model of Hele–Shaw type, a variant including growth terms, starting from the description at the cell level and passing to the stiff limit in the pressure law of state. In contrast with the classical Hele–Shaw problem, here the geometric motion governed by the pressure is not sufficient to completely describe the dynamics. A complete description requires the equation on the cell number density. We then go on to consider a more complex model including the supply of nutrients through vasculature, and we study the stiff limit for the involved coupled system.
      PubDate: 2014-01-14
       
  • The Γ-Limit of the Two-Dimensional Ohta–Kawasaki Energy.
           Droplet Arrangement via the Renormalized Energy
    • Abstract: This is the second in a series of papers in which we derive a Γ-expansion for the two-dimensional non-local Ginzburg–Landau energy with Coulomb repulsion known as the Ohta–Kawasaki model in connection with diblock copolymer systems. In this model, two phases appear, which interact via a nonlocal Coulomb type energy. Here we focus on the sharp interface version of this energy in the regime where one of the phases has very small volume fraction, thus creating small “droplets” of the minority phase in a “sea” of the majority phase. In our previous paper, we computed the Γ-limit of the leading order energy, which yields the averaged behavior for almost minimizers, namely that the density of droplets should be uniform. Here we go to the next order and derive a next order Γ-limit energy, which is exactly the Coulombian renormalized energy obtained by Sandier and Serfaty as a limiting interaction energy for vortices in the magnetic Ginzburg–Landau model. The derivation is based on the abstract scheme of Sandier-Serfaty that serves to obtain lower bounds for 2-scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem. Thus, without appealing to the Euler–Lagrange equation, we establish for all configurations which have “almost minimal energy” the asymptotic roundness and radius of the droplets, and the fact that they asymptotically shrink to points whose arrangement minimizes the renormalized energy in some averaged sense. Via a kind of Γ-equivalence, the obtained results also yield an expansion of the minimal energy and a characterization of the zero super-level sets of the minimizers for the original Ohta–Kawasaki energy. This leads to the expectation of seeing triangular lattices of droplets as energy minimizers.
      PubDate: 2014-01-14
       
  • On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic
           Potentials and Time Averaging
    • Abstract: Abstract We analyse a nonlinear Schrödinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree–Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schrödinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.
      PubDate: 2014-01-14
       
  • On Finite Time Singularity and Global Regularity of an Axisymmetric Model
           for the 3D Euler Equations
    • Abstract: Abstract In (Comm Pure Appl Math 62(4):502–564, 2009), Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier–Stokes equations with swirl. This model shares a number of properties of the 3D incompressible Euler and Navier–Stokes equations. In this paper, we prove that the 3D inviscid model with an appropriate Neumann-Robin or Dirichlet-Robin boundary condition will develop a finite time singularity in an axisymmetric domain. We also provide numerical confirmation for our finite time blowup results. We further demonstrate that the energy of the blowup solution is bounded up to the singularity time, and the blowup mechanism for the mixed Dirichlet-Robin boundary condition is essentially the same as that for the energy conserving homogeneous Dirichlet boundary condition. Finally, we prove that the 3D inviscid model has globally smooth solutions for a class of large smooth initial data with some appropriate boundary condition. Both the analysis and the results we obtain here improve the previous work in a rectangular domain by Hou et al. (Adv Math 230:607–641, 2012) in several respects.
      PubDate: 2014-01-09
       
  • Pointwise Bounds for the Solutions of the Smoluchowski Equation with
           Diffusion
    • Abstract: Abstract We prove various decay bounds on solutions (f n : n > 0) of the discrete and continuous Smoluchowski equations with diffusion. More precisely, we establish pointwise upper bounds on n ℓ f n in terms of a suitable average of the moments of the initial data for every positive ℓ. As a consequence, we can formulate sufficient conditions on the initial data to guarantee the finiteness of ${L^p(\mathbb{R}^d \times [0, T])}$ norms of the moments ${X_a(x, t) := \sum_{m\in\mathbb{N}}m^a f_m(x, t)}$ , ( ${\int_0^{\infty} m^a f_m(x, t)dm}$ in the case of continuous Smoluchowski’s equation) for every ${p \in [1, \infty]}$ . In previous papers [11] and [5] we proved similar results for all weak solutions to the Smoluchowski’s equation provided that the diffusion coefficient d(n) is non-increasing as a function of the mass. In this paper we apply a new method to treat general diffusion coefficients and our bounds are expressed in terms of an auxiliary function ${\phi(n)}$ that is closely related to the total increase of the diffusion coefficient in the interval (0, n].
      PubDate: 2014-01-09
       
  • Regularity and Asymptotic Behavior of Nonlinear Stefan Problems
    • Abstract: Abstract We study the following nonlinear Stefan problem $$\left\{\begin{aligned}\!\!&u_t\,-\,d\Delta u = g(u) & &\quad{\rm for}\,x\,\in\,\Omega(t), t > 0, \\ & u = 0 \, {\rm and} u_t = \mu \nabla_{x} u ^{2} &&\quad {\rm for}\,x\,\in\,\Gamma(t), t > 0, \\ &u(0, x) = u_{0}(x) &&\quad {\rm for}\,x\,\in\,\Omega_0,\end{aligned} \right.$$ where ${\Omega(t) \subset \mathbb{R}^{n}}$ ( ${n \geqq 2}$ ) is bounded by the free boundary ${\Gamma(t)}$ , with ${\Omega(0) = \Omega_0}$ , μ and d are given positive constants. The initial function u 0 is positive in ${\Omega_0}$ and vanishes on ${\partial \Omega_0}$ . The class of nonlinear functions g(u) includes the standard monostable, bistable and combustion type nonlinearities. We show that the free boundary ${\Gamma(t)}$ is smooth outside the closed convex hull of ${\Omega_0}$ , and as ${t \to \infty}$ , either ${\Omega(t)}$ expands to the entire ${\mathbb{R}^n}$ , or it stays bounded. Moreover, in the former case, ${\Gamma(t)}$ converges to the unit sphere when normalized, and in the latter case, ${u \to 0}$ uniformly. When ${g(u) = au - bu^2}$ , we further prove that in the case ${\Omega(t)}$ expands to ${{\mathbb R}^n}$ , ${u \to a/b}$ as ${t \to \infty}$ , and the spreading speed of the free boundary converges to a positive constant; moreover, there exists ${\mu^* \geqq 0}$ such that ${\Omega(t)}$ expands to ${{\mathbb{R}}^n}$ exactly when ${\mu > \mu^*}$ .
      PubDate: 2014-01-08
       
  • A Perturbation Argument for a Monge–Ampère Type Equation
           Arising in Optimal Transportation
    • Abstract: Abstract We prove some interior regularity results for potential functions of optimal transportation problems with power costs. The main point is that our problem is equivalent to a new optimal transportation problem whose cost function is a sufficiently small perturbation of the quadratic cost, but it does not satisfy the well known condition (A.3) guaranteeing regularity. The proof consists in a perturbation argument from the standard Monge–Ampère equation in order to obtain, first, interior C1,1 estimates for the potential and, second, interior Hölder estimates for second derivatives. In particular, we take a close look at the geometry of optimal transportation when the cost function is close to quadratic in order to understand how the equation degenerates near the boundary.
      PubDate: 2014-01-08
       
  • Phase Transitions and Traveling Waves in Compressible Fluids
    • Abstract: Abstract This note studies families of isothermal Navier–Stokes–Allen–Cahn systems that are parameterized by temperature. It shows that under natural assumptions, the possibility of traveling waves corresponding to phase boundaries arises during a phase transition at a critical temperature. Below that temperature, besides pairs of “Maxwell” states connected by waves with zero net mass flux, there exist also interfaces across which particles undergo a phase transformation.
      PubDate: 2014-01-01
       
 
 
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