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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 ... -
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 ... -
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 ... -
Full characterization of the fractional Poisson process
(2011-12-31)The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied ... -
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 ... -
Flux identification for 1-d scalar conservation laws in the presence of shocks
(2011-12-31)We consider the problem of flux identification for 1-d scalar conservation laws formulating it as an optimal control problem. We introduce a new optimization strategy to compute numerical approximations of minimizing fluxes. ... -
Propagation of chaos in a coagulation model
(2013-12-31)The dynamics of a finite system of coalescing particles in a finite volume is considered. It is shown that, in the thermodynamic limit, a coagulation equation is recovered and propagation of chaos holds for all time. -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ...