### Recent Submissions

• #### A splitting method for the augmented Burgers equation ﻿

(2017-07-01)
In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of ﬁrst order. We also analyze the large-time behavior of the approximated solution by obtaining the ﬁrst term in the ...
• #### A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation ﻿

(2017-06-01)
In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain $L^1-L^p$ decay rates. The asymptotic behavior of the solution is ...
• #### Spherically symmetric solutions to a model for phase transitions driven by configurational forces ﻿

(2011-12-31)
We prove the global-in-time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a ...
• #### Approximation of Hölder continuous homeomorphisms by piecewise affine homeomorphisms ﻿

(2011-12-31)
This paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to ℝ2 that is ...
• #### A splitting method for the nonlinear Schrödinger equation ﻿

(2011-12-31)
We introduce a splitting method for the semilinear Schrödinger equation and prove its convergence for those nonlinearities which can be handled by the classical well-posedness L2(Rd)-theory. More precisely, we prove that ...
• #### Dispersive Properties for Discrete Schrödinger Equations ﻿

(2011-12-31)
In this paper we prove dispersive estimates for the system formed by two coupled discrete Schrödinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting ...
• #### Solvability via viscosity solutions for a model of phase transitions driven by configurational forces ﻿

(2011-12-31)
This article is concerned with an initial-boundary value problem for an elliptic-parabolic coupled system arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel. This model ...
• #### The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide ﻿

(2011-12-31)
We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay ...
• #### Interface motion by interface diffusion driven by bulk energy: Justification of a diffusive interface model ﻿

(2011-12-31)
We construct an asymptotic solution of a system consisting of the partial differential equations of linear elasticity theory coupled with a degenerate parabolic equation, and show that when a regularity parameter tends to ...
• #### Homogenization of the Neumann problem in perforated domains: An alternative approach ﻿

(2011-12-31)
The main result of this paper is a compactness theorem for families of functions in the space SBV (Special functions of Bounded Variation) defined on periodically perforated domains. Given an open and bounded set Ω n, and ...
• #### Stationary policies for the second moment stability in a class of stochastic systems ﻿

(2011-12-31)
This paper presents a study on the uniform second moment stability for a class of stochastic control system. The main result states that the existence of the long-run average cost under a stationary policy is equivalent ...
• #### A kinetic scheme for transient mixed flows in non uniform closed pipes: A global manner to upwind all the source terms ﻿

(2011-12-31)
We present a numerical kinetic scheme for an unsteady mixed pressurized and free surface model. This model has a source term depending on both the space variable and the unknown U of the system. Using the Finite Volume and ...
• #### Nematic elastomers: Gamma-limits for large bodies and small particles ﻿

(2011-12-31)
We compute the large-body and the small-particle Gamma-limit of a family of energies for nematic elastomers. We work under the assumption of small deformations (linearized kinematics) and consider both compressible and ...
• #### Well-posedness in critical spaces for the system of compressible Navier-Stokes in larger spaces ﻿

(2011-12-31)
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N≥2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves the analysis ...
• #### Low Mach number limit of viscous polytropic fluid flows ﻿

(2011-12-31)
This paper studies the singular limit of the non-isentropic Navier-Stokes equations with zero thermal coefficient in a two-dimensional bounded domain as the Mach number goes to zero. A uniform existence result is obtained ...
• #### Dispersion for the Schrödinger equation on networks ﻿

(2011-12-31)
In this paper, we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schrödinger ...
• #### Compressible primitive equations: Formal derivation and stability of weak solutions ﻿

(2011-12-31)
We present a formal derivation of compressible primitive equations for atmosphere modelling. They are obtained from the 3D compressible Navier- Stokes equations with an anisotropic viscous stress tensor depending on the ...
• #### Traveling waves to models of solid-solid phase transitions driven by configurational forces ﻿

(2011-12-31)
We study the existence of traveling/standing waves to models based on configurational forces. These models describe, respectively, structural phase transitions in solids, e.g., Shape memory alloys, and phase transitions ...
• #### Best constants and Pohozaev identity for hardy-sobolev-type operators ﻿

(2013-12-31)
This paper is threefold. Firstly, we reformulate the definition of the norm induced by the Hardy inequality (see [J. L. Vázquez and N. B. Zographopoulos, Functional aspects of the Hardy inequality. Appearance of a hidden ...
• #### Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications ﻿

(2011-12-31)
We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the ...