Subjects -> MATHEMATICS (Total: 1118 journals)     - APPLIED MATHEMATICS (92 journals)    - GEOMETRY AND TOPOLOGY (23 journals)    - MATHEMATICS (819 journals)    - MATHEMATICS (GENERAL) (45 journals)    - NUMERICAL ANALYSIS (26 journals)    - PROBABILITIES AND MATH STATISTICS (113 journals) MATHEMATICS (819 journals)                  1 2 3 4 5 | Last

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 Applied Mathematics & OptimizationJournal Prestige (SJR): 0.886 Citation Impact (citeScore): 1Number of Followers: 13      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1432-0606 - ISSN (Online) 0095-4616 Published by Springer-Verlag  [2658 journals]
• A General Stability Result for a Viscoelastic Moore–Gibson–Thompson
Equation in the Whole Space

Abstract: In this paper, we are interested in a viscoelastic Moore–Gibson–Thompson equation with a type-II memory term and a relaxation function satisfying $$g^{\prime }(t)\le -\eta (t)g(t)$$ . By constructing appropriate Lyapunov functionals in the Fourier space, we establish a general decay estimate of the solution under the condition $$\left( \beta -\frac{\gamma }{\alpha }-\frac{\varrho }{2}\right) >0.$$ We then give the decay rate of the L $$^{2}$$ -norm of the solution. We also give two examples to illustrate our theoretical results.
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09777-5

• Large Deviation Principle for McKean–Vlasov Quasilinear Stochastic
Evolution Equations

Abstract: This paper is devoted to investigating the Freidlin–Wentzell’s large deviation principle for a class of McKean–Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak convergence criteria to prove the Laplace principle for McKean–Vlasov type SPDEs, which is equivalent to the large deviation principle. Moreover, we do not assume any compactness condition of embedding in the Gelfand triple to handle both the cases of bounded and unbounded domains in applications. The main results can be applied to various McKean–Vlasov type SPDEs such as distribution dependent stochastic porous media type equations and stochastic p-Laplace type equations.
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09796-2

• Normality, Controllability and Properness in Optimal Control

Abstract: In this paper we show that, for optimal control problems involving equality and inequality constraints on the control function, the notions of normality and properness (or the Mangasarian–Fromovitz constraint qualification) of a trajectory relative to the set of constraints are equivalent. This is in contrast with some differences recently obtained between the theories of mathematical programming and optimal control, and it provides an important insight in the derivation of first and second order necessary optimality conditions for infinite dimensional problems.
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09765-9

• Exploiting Characteristics in Stationary Action Problems

Abstract: Connections between the principle of least action and optimal control are explored with a view to describing the trajectories of energy conserving systems, subject to temporal boundary conditions, as solutions of corresponding systems of characteristics equations on arbitrary time horizons. Motivated by the relaxation of least action to stationary action for longer time horizons, due to loss of convexity of the action functional, a corresponding relaxation of optimal control problems to stationary control problems is considered. In characterizing the attendant stationary controls, corresponding to generalized velocity trajectories, an auxiliary stationary control problem is posed with respect to the characteristic system of interest. Using this auxiliary problem, it is shown that the controls rendering the action functional stationary on arbitrary time horizons have a state feedback representation, via a verification theorem, that is consistent with the optimal control on short time horizons. An example is provided to illustrate application via a simple mass-spring system.
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09784-6

• Boussinesq System with Partial Viscous Diffusion or Partial Thermal
Diffusion Forced by a Random Noise

Abstract: We study the Boussinesq system in a two-dimensional domain. In case only the velocity equation is forced by a white-in-time multiplicative noise, we prove the global existence of a martingale solution in the following two cases: positive horizontal viscous diffusion but zero vertical viscous diffusion and zero thermal diffusion; positive horizontal thermal diffusion but zero viscous diffusion and zero vertical thermal diffusion. Finally, in case both velocity and temperature equations are forced by a white-in-time multiplicative noise, and the velocity equation has zero viscous diffusion while the temperature equation has full thermal diffusion, the global existence of a martingale solution was shown in Yamazaki (Stoch Anal Appl, 34:404–426, 2016); in this manuscript we additionally prove significantly higher regularity.
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09756-w

• Structural Stability in Resonant Penetrative Convection in a
Brinkman–Forchheimer Fluid Interfacing with a Darcy Fluid

Abstract: The resonant penetrative convection in a Brinkman–Forchheimer fluid interfacing with a Darcy fluid is considered. It is our main purpose to study the continuous dependence of the solution on changes in the heat source and the continuous dependence of the solution on the Forchheimer coefficient.
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09791-7

• Existence of Ground State Sign-Changing Solutions of Fractional
Kirchhoff-Type Equation with Critical Growth

Abstract: In this paper, we study the following fractional Kirchhoff-type equation \begin{aligned}{\left\{ \begin{array}{ll} -(a+ b\int _{{\mathbb {R}}^{N}}\int _{{\mathbb {R}}^{N}} u(x)-u(y) ^{2}K(x-y)dxdy){\mathcal {L}}_{K}u= u ^{2_{\alpha }^{*}-2}u+\mu f(u), ~\ x\in \Omega ,\\ u=0, ~\ x\in {\mathbb {R}}^{N}\backslash \Omega , \end{array}\right. } \end{aligned} where $$\Omega \subset {\mathbb {R}}^{N}$$ is a bounded domain with a smooth boundary, $$\alpha \in (0,1)$$ , $$2\alpha<N<4\alpha$$ , $$2_{\alpha }^{*}$$ is the fractional critical Sobolev exponent and $$\mu , a, b>0$$ ; $${\mathcal {L}}_{K}$$ is non-local integrodifferential operator. Under suitable conditions on f, for $$\mu$$ large enough, by using constraint variational method and the quantitative deformation lemma, we obtain a ground state sign-changing (or nodal) solution to this problem, and its energy is strictly larger than twice that of the ground state solutions.
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09763-x

• Spectral Stability for the Peridynamic Fractional p-Laplacian

Abstract: In this work we analyze the behavior of the spectrum of the peridynamic fractional p-Laplacian, $$(-\Delta _p)_{\delta }^{s}$$ , under the limit process $$\delta \rightarrow 0^+$$ or $$\delta \rightarrow +\infty$$ . We prove spectral convergence to the classical p-Laplacian under a suitable scaling as $$\delta \rightarrow 0^+$$ and to the fractional p-Laplacian as $$\delta \rightarrow +\infty$$ .
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09768-6

• Correction To: Existence Results for Fractional p(x, .)-Laplacian Problem
Via the Nehari Manifold Approach

PubDate: 2021-12-01
DOI: 10.1007/s00245-020-09725-9

• Correction to: Stochastic Maximum Principle Under Probability Distortion

PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09795-3

• Correction to: Convergence Analysis of a Crank–Nicolson Galerkin Method
for an Inverse Source Problem for Parabolic Equations with Boundary
Observations

Abstract: The original version of this article unfortunately contained a mistake in one of the co-author’s name.
PubDate: 2021-12-01
DOI: 10.1007/s00245-020-09717-9

• Correction to: Optimal Control of a Phase Field System Modelling Tumor
Growth with Chemotaxis and Singular Potentials

Abstract: A Correction to this paper has been published: https://doi.org/10.1007/s00245-019-09618-6
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09771-x

• Correction to: On Nonlocal Variational and Quasi-Variational Inequalities

Abstract: A Correction to this paper has been published: https://doi.org/10.1007/s00245-019-09610-0
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09760-0

• Sensitivity Analysis of Optimal Control Problems Governed by Nonlinear
Hilfer Fractional Evolution Inclusions

Abstract: This article studies sensitivity properties of optimal control problems that are governed by nonlinear Hilfer fractional evolution inclusions (NHFEIs) in Hilbert spaces, where the initial state $$\xi$$ is not the classical Cauchy, but is the Riemann–Liouville integral. First, we obtain the nonemptiness and the compactness properties of mild solution sets $$\mathbb {S}(\xi )$$ for NHFEIs, and also establish an extension Filippov’s theorem. Then we obtain the continuity and upper semicontinuity of optimal control problems connected with NHFEIs depending on a initial state $$\xi$$ as well as a parameter $$\lambda$$ . Finally, An illustrating example is given.
PubDate: 2021-12-01
DOI: 10.1007/s00245-020-09739-3

• Exponential Stabilization of the Wave Equation on Hyperbolic Spaces with
Nonlinear Locally Distributed Damping

Abstract: In this article, we consider the wave equation on hyperbolic spaces $$\mathbb {H}^n(n\ge 2)$$ with nonlinear locally distributed damping as follow: 1 \begin{aligned} {\left\{ \begin{array}{ll}u_{tt}-\Delta _g u+a(x)g(u_t)=0\qquad (x,t)\in \mathbb {H}^n\times (0,+\infty ), \\ u(x,0)=u_0(x),\quad u_0(x,0)=u_1(x)\qquad x\in \mathbb {H}^n. \end{array}\right. } \end{aligned} It is well-known that the energy of the system (1) is of polynomial decay in the Euclidean space. However, on hyperbolic spaces, owing to the following inequality 2 \begin{aligned} \int _{\mathbb {H}^n} u^2 dx_g \le C \int _{\mathbb {H}^n} \nabla _g u _g^2dx_g , \quad for \quad u\in H^1(\mathbb {H}^n), \end{aligned} we prove the exponential stabilization of the wave equation by multiplier methods and compactness-uniqueness arguments.
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09751-1

• About Symmetry in Partially Hinged Composite Plates

Abstract: We consider a partially hinged composite plate problem and we investigate qualitative properties, e.g. symmetry and monotonicity, of the eigenfunction corresponding to the density minimizing the first eigenvalue. The analysis is performed by showing related properties of the Green function of the operator and by applying polarization with respect to a fixed plane. As a by-product of the study, we obtain a Hopf type boundary lemma for the operator having its own theoretical interest. The statements are complemented by numerical results.
PubDate: 2021-12-01
DOI: 10.1007/s00245-020-09722-y

• Some Inequalities Involving Perimeter and Torsional Rigidity

Abstract: We consider shape functionals of the form $$F_q(\Omega )=P(\Omega )T^q(\Omega )$$ on the class of open sets of prescribed Lebesgue measure. Here $$q>0$$ is fixed, $$P(\Omega )$$ denotes the perimeter of $$\Omega$$ and $$T(\Omega )$$ is the torsional rigidity of $$\Omega$$ . The minimization and maximization of $$F_q(\Omega )$$ is considered on various classes of admissible domains $$\Omega$$ : in the class $$\mathcal {A}_{all}$$ of all domains, in the class $$\mathcal {A}_{convex}$$ of convex domains, and in the class $$\mathcal {A}_{thin}$$ of thin domains.
PubDate: 2021-12-01
DOI: 10.1007/s00245-020-09727-7

• (p, q)-Equations with Singular and Concave Convex Nonlinearities

Abstract: We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian with $$1<q<p$$ . The reaction is parametric and exhibits the competing effects of a singular term and of concave and convex nonlinearities. We are looking for positive solutions and prove a bifurcation-type theorem describing in a precise way the set of positive solutions as the parameter varies. Moreover, we show the existence of a minimal positive solution and we study it as a function of the parameter.
PubDate: 2021-12-01
DOI: 10.1007/s00245-020-09720-0

• On the Exponential Stability of Stochastic Perturbed Singular Systems in
Mean Square

Abstract: The approach of Lyapunov functions is one of the most efficient ones for the investigation of the stability of stochastic systems, in particular, of singular stochastic systems. The main objective of the paper is the analysis of the stability of stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. The uniform exponential stability in mean square and the practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems based on Lyapunov techniques are investigated. Moreover, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, an illustrative example is given to illustrate the effectiveness of the proposed results.
PubDate: 2021-12-01
DOI: 10.1007/s00245-020-09734-8

• Existence and Continuity of Inertial Manifolds for the Hyperbolic
Relaxation of the Viscous Cahn–Hilliard Equation

Abstract: We consider the hyperbolic relaxation of the viscous Cahn–Hilliard equation 0.1 \begin{aligned} \varepsilon \phi _{tt}+ \phi _t-\Delta (\delta \phi _t-\Delta \phi + g(\phi ))=0, \end{aligned} in a bounded domain of $${\mathbb R}^d$$ with smooth boundary when subject to Neumann boundary conditions, and on rectangular domains when subject to periodic boundary conditions. The space dimension is $$d=1,$$ 2 or 3, but it is required $$\delta =\varepsilon =0$$ when $$d=2$$ or 3; $$\delta$$ being the viscosity parameter. The constant $$\varepsilon \in (0,1]$$ is a relaxation parameter, $$\phi$$ is the order parameter and $$g:{\mathbb R}\rightarrow {\mathbb R}$$ is a nonlinear function. This equation models the early stages of spinodal decomposition in certain glasses. Assuming that $$\varepsilon$$ is dominated from above by $$\delta$$ when $$d=2$$ or 3, we construct a family of exponential attractors for Eq. (0.1) which converges as $$(\varepsilon ,\delta )$$ goes to $$(0,\delta _0),$$ for any $$\delta _0\in [0,1],$$ with respect to a metric that depends only on $$\varepsilon$$ , improving previous results where this metric also depends on $$\delta$$ . Then we introduce two change of variables and corresponding problems, in the case of rectangular domains and $$d=1$$ or 2 only. First, we set $$\tilde{\phi }(t)=\phi (\sqrt{\varepsilon } t)$$ and we rewrite Eq. (0.1) in the variables $$(\tilde{\phi },\tilde{\phi }_t).$$ We show that there exist an integer n, independent of both $$\varepsilon$$ and $$\delta$$ , a value $$0<\tilde{\varepsilon }_0(n)\le 1$$ and an inertial manifold of dimension n, for either $$\varepsilon \in (0,\tilde{\varepsilon }_0]$$ and $$\delta =2\sqrt{\varepsilon }$$ or $$\varepsilon \in (0,\tilde{\varepsilon }_0]$$ and $$\delta \in [0,3\varepsilon ]$$ . Then, we prove the e...
PubDate: 2021-12-01
DOI: 10.1007/s00245-021-09749-9

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