Abstract: The standard model has the deficiency of predicting swirling and vortical flows due to its isotropic assumption of eddy viscosity. In this study, a second-order nonlinear model is developed incorporating some new functions for the model coefficients to explore the models applicability to complex turbulent flows. Considering the realizability principle, the coefficient of eddy viscosity () is derived as a function of strain and rotation parameters. The coefficients of nonlinear quadratic term are estimated considering the anisotropy of turbulence in a simple shear layer. Analytical solutions for the fundamental properties of swirl jet are derived based on the nonlinear model, and the values of model constants are determined by tuning their values for the best-fitted comparison with the experiments. The model performance is examined for two test cases: (i) for an ideal vortex (Stuart vortex), the basic equations are solved numerically to predict the turbulent structures at the vortex center and the (ii) unsteady 3D simulation is carried out to calculate the flow field of a compound channel. It is observed that the proposed nonlinear model can successfully predict the turbulent structures at vortex center, while the standard model fails. The model is found to be capable of accounting the effect of transverse momentum transfer in the compound channel through generating the horizontal vortices at the interface. PubDate: Thu, 19 Feb 2015 09:47:11 +000

Abstract: We continue our study of the complex Monge-Ampère operator on the weighted pluricomplex energy classes. We give more characterizations of the range of the classes by the complex Monge-Ampère operator. In particular, we prove that a nonnegative Borel measure is the Monge-Ampère of a unique function if and only if . Then we show that if for some then for some , where is given boundary data. If moreover the nonnegative Borel measure is suitably dominated by the Monge-Ampère capacity, we establish a priori estimates on the capacity of sublevel sets of the solutions. As a consequence, we give a priori bounds of the solution of the Dirichlet problem in the case when the measure has a density in some Orlicz space. PubDate: Tue, 10 Feb 2015 09:42:02 +000

Abstract: We proposed numerical methods for solving the direct and inversescattering problems for domains with multiple corners. Both the nearfield and far field cases are considered. For the forward problem, thechallenges of logarithmic singularity from Green’s functions and cornersingularity are both taken care of. For the inverse problem, an efficientand robust direct imaging method is proposed. Multiple frequency dataare combined to capture details while not losing robustness. PubDate: Mon, 26 Jan 2015 13:46:02 +000

Abstract: Working in a weighted Sobolev space, this paper is devoted to the study of the boundary value problem for the quasilinear parabolic equations with superlinear growth conditions in a domain of . Some conditions which guarantee the solvability of the problem are given. PubDate: Sun, 21 Dec 2014 08:43:56 +000

Abstract: We construct a new method for inextensible flows of timelike curves in Minkowski space-time . Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a timelike curve in Minkowski space-time . PubDate: Tue, 16 Dec 2014 13:43:41 +000

Abstract: We employ the multiplier approach (variational derivative method) to derive the conservation laws for the Degasperis Procesi equation and a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model. Firstly, the multipliers are computed and then conserved vectors are obtained for each multiplier. PubDate: Thu, 13 Nov 2014 07:49:11 +000

Abstract: The modified decomposition method (MDM) is improved by introducing new inverse differential operators to adapt the MDM for handling third-order singular nonlinear partial differential equations (PDEs) arising in physics and mechanics. A few case-study singular nonlinear initial-value problems (IVPs) of third-order PDEs are presented and solved by the improved modified decomposition method (IMDM). The solutions are compared with the existing exact analytical solutions. The comparisons show that the IMDM is effectively capable of obtaining the exact solutions of the third-order singular nonlinear IVPs. PubDate: Thu, 06 Nov 2014 00:00:00 +000

Abstract: We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say, , with , , then the solution is in fact smooth. This improves previous results greatly. PubDate: Mon, 27 Oct 2014 00:00:00 +000

Abstract: The research on spectral inequalities for discrete Schrödinger operators has proved fruitful in the last decade. Indeed, several authors analysed the operator’s canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we consider a generalisation of this relation with regard to connecting higher order Schrödinger-type operators with symmetric matrix operators with arbitrarily many nonzero diagonals above and below the main diagonal. We thus obtain spectral bounds for such matrices, similar in nature to the Lieb-Thirring inequalities. PubDate: Sun, 19 Oct 2014 11:42:05 +000

Abstract: In this work we present an application of a theory of vessels to a solution of the evolutionary nonlinear Schrödinger (NLS) equation. The classes of functions for which the initial value problem is solvable rely on the existence of an analogue of the inverse scattering theory for the usual NLS equation. This approach is similar to the classical approach of Zakharov-Shabath for solving evolutionary NLS equation but has an advantage of simpler formulas and new techniques and notions to understand the solutions. PubDate: Tue, 07 Oct 2014 00:00:00 +000

Abstract: This paper is divided in two parts. In the first part we study a second order neutral partial differential equation with state dependent delay and noninstantaneous impulses. The conditions for existence and uniqueness of the mild solution are investigated via Hausdorff measure of noncompactness and Darbo Sadovskii fixed point theorem. Thus we remove the need to assume the compactness assumption on the associated family of operators. The conditions for approximate controllability are investigated for the neutral second order system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. A simple range condition is used to prove approximate controllability. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in (Balachandran and Park, 2003), which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in (Dauer and Mahmudov, 2002), which are practically difficult to verify and apply. Examples are provided to illustrate the presented theory. PubDate: Thu, 02 Oct 2014 13:22:58 +000

Abstract: Modified cubic B-spline collocation method is discussed for the numerical solution of one-dimensional nonlinear sine-Gordon equation. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. The given equation is decomposed into a system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of ordinary differential equations. The resulting system of equation has subsequently been solved by SSP-RK54 scheme. The efficacy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and are in good agreement with earlier studies. PubDate: Sun, 10 Aug 2014 06:23:46 +000

Abstract: We obtain the numerical solution of a Boussinesq system fortwo-way propagation of nonlinear dispersive waves by using the meshlessmethod, based on collocation with radial basis functions. The system ofnonlinear partial differential equation is discretized in space by approximatingthe solution using radial basis functions. The discretization leads to asystem of coupled nonlinear ordinary differential equations. The equationsare then solved by using the fourth-order Runge-Kutta method. A stabilityanalysis is provided and then the accuracy of method is tested by comparingit with the exact solitary solutions of the Boussinesq system. In addition, theconserved quantities are calculated numerically and compared to an exactsolution. The numerical results show excellent agreement with the analyticalsolution and the calculated conserved quantities. PubDate: Sun, 03 Aug 2014 08:28:41 +000

Abstract: We present a new technique to obtain the solution of time-fractional coupled Schrödinger system. The fractional derivatives are considered in Caputo sense. The proposed scheme is based on Laplace transform and new homotopy perturbation method. To illustrate the power and reliability of the method some examples are provided. The results obtained by the proposed method show that the approach is very efficient and simple and can be applied to other partial differential equations. PubDate: Tue, 15 Jul 2014 00:00:00 +000

Abstract: The Bitsadze-Samarskii nonlocal boundary value problem is considered. Variational formulation is done. The domain decomposition and Schwarz-type iterative methods are used. The parallel algorithm as well as sequential ones is investigated. PubDate: Thu, 19 Jun 2014 13:33:37 +000

Abstract: We study the existence of solutions of impulsive semilinear differential equation in a Banach space in which impulsive condition is not instantaneous. We establish the existence of a mild solution by using the Hausdorff measure of noncompactness and a fixed point theorem for the convex power condensing operator. PubDate: Sun, 18 May 2014 11:11:20 +000

Abstract: We derive general bounds for the large time size of supnorm values of solutions to one-dimensional advection-diffusion equations with initial data for some and arbitrary bounded advection speeds , introducing new techniques based on suitable energy arguments. Some open problems and related results are also given. PubDate: Thu, 08 May 2014 11:18:52 +000

Abstract: We deal with the existence of quantitative estimates for solutions of mixed problems to an elliptic second-order equation in divergence form with discontinuous coefficients. Our concern is to estimate the solutions with explicit constants, for domains in () of class . The existence of and estimates is assured for and any (depending on the data), whenever the coefficient is only measurable and bounded. The proof method of the quantitative estimates is based on the De Giorgi technique developed by Stampacchia. By using the potential theory, we derive estimates for different ranges of the exponent depending on the fact that the coefficient is either Dini-continuous or only measurable and bounded. In this process, we establish new existences of Green functions on such domains. The last but not least concern is to unify (whenever possible) the proofs of the estimates to the extreme Dirichlet and Neumann cases of the mixed problem. PubDate: Mon, 31 Mar 2014 11:15:41 +000

Abstract: We consider initial boundary value problem for a reaction-diffusion system with nonlinear and nonlocal boundary conditions and nonnegative initial data. We prove local existence, uniqueness, and nonuniqueness of solutions. PubDate: Thu, 20 Feb 2014 07:02:08 +000

Abstract: We prove that one system of coupled KdV equations, claimed by Hirota et al. to pass the Painlevé test for integrability, actually fails the test at the highest resonance of the generic branch and therefore must be nonintegrable. PubDate: Wed, 19 Feb 2014 11:23:52 +000

Abstract: The aim of this paper is to study the dynamics of a reaction-diffusion SIR epidemic model with specific nonlinear incidence rate. The global existence, positivity, and boundedness of solutions for a reaction-diffusion system with homogeneous Neumann boundary conditions are proved. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. By means of Lyapunov functional, the global stability of both equilibria is investigated. More precisely, our results show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than or equal to unity, which leads to the eradication of disease from population. When the basic reproduction number is greater than unity, then disease-free equilibrium becomes unstable and the endemic equilibrium is globally asymptotically stable; in this case the disease persists in the population. Numerical simulations are presented to illustrate our theoreticalresults. PubDate: Mon, 10 Feb 2014 09:59:55 +000

Abstract: A semilinear parabolic transmission problem with Ventcel's boundary conditions on a fractal interface or the corresponding prefractal interface is studied. Regularity results for the solution in both cases are proved. The asymptotic behaviour of the solutions of the approximating problems to the solution of limit fractal problem is analyzed. PubDate: Wed, 22 Jan 2014 08:09:38 +000

Abstract: The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. In this paper, we present a mixed finite volume element method (FVEM) for the approximation of thepressure-velocity equation. Since modified method of characteristics (MMOC) minimizes the grid orientation effect, for the approximation of the concentration equation, we apply a standard FVEM combined with MMOC. A priori error estimates in norm are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results. PubDate: Sun, 19 Jan 2014 00:00:00 +000

Abstract: We consider the Cauchy problem for an integrable modified two-component Camassa-Holm system with cubic nonlinearity. By using the Littlewood-Paley decomposition, nonhomogeneous Besov spaces, and a priori estimates for linear transport equation, we prove that the Cauchy problem is locally well-posed in Besov spaces with , and . PubDate: Tue, 31 Dec 2013 17:48:27 +000

Abstract: In this paper, we analyze some initial-boundary value problems forthe subdiffusion equation with a fractional dynamic boundary condition in aone-dimensional bounded domain. First, we establish the unique solvabilityin the Hölder space of the initial-boundary value problems for the equation , , where L is a uniformly ellipticoperator with smooth coefficients with the fractional dynamic boundary condition. Second, we apply the contraction theorem to prove the existence anduniqueness locally in time in the Hölder classes of the solution to the corresponding nonlinear problems. PubDate: Thu, 07 Nov 2013 09:00:04 +000

Abstract: We apply Rothe’s type fixed point theorem to prove the interior approximate controllability of the following semilinear heat equation: in on , where is a bounded domain in , , is an open nonempty subset of , denotes the characteristic function of the set , the distributed control belongs to , and the nonlinear function is smooth enough, and there are , and such that for all Under this condition, we prove the following statement: for all open nonempty subset of , the system is approximately controllable on . Moreover, we could exhibit a sequence of controls steering the nonlinear system from an initial state to an neighborhood of the final state at time . PubDate: Sun, 03 Nov 2013 14:56:58 +000

Abstract: In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions. PubDate: Thu, 10 Oct 2013 15:55:46 +000

Abstract: The nonlinear dispersive Boussinesq-like equation , which exhibits single peak solitons, is investigated. Peakons, cuspons and smooth soliton solutions are obtained by setting the equation under inhomogeneous boundary condition. Asymptotic behavior and numerical simulations are provided for these three types of single peak soliton solutions of the equation. PubDate: Wed, 09 Oct 2013 12:00:32 +000

Abstract: We consider the problem of determining an unknown source which depends only on one variable in two-dimensional Poisson equation. We prove a conditional stability for this problem. Moreover, we propose a truncation regularization method combined with an a posteriori regularization parameter choice rule to deal with this problem and give the corresponding convergence estimate. Numerical results are presented to illustrate the accuracy and efficiency of this method. PubDate: Thu, 19 Sep 2013 10:53:25 +000

Abstract: By method of integral equations, unique solvability is proved for the solution of boundary value problems of loaded third-order integrodifferential equations with Riemann-Liouville operators. PubDate: Sun, 08 Sep 2013 08:54:18 +000