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A semidiscrete largetime behavior preserving scheme for the augmented Burgers equation
(ESAIM: Mathematical Modelling and Numerical Analysis, 20170601)In this paper we analyze the largetime behavior of the augmented Burgers equation. We first study the wellposedness of the Cauchy problem and obtain $L^1L^p$ decay rates. The asymptotic behavior of the solution is ... 
Flux identification for 1d scalar conservation laws in the presence of shocks
(Mathematics of Computation, 20111231)We consider the problem of flux identification for 1d scalar conservation laws formulating it as an optimal control problem. We introduce a new optimization strategy to compute numerical approximations of minimizing fluxes. ... 
Regularity issues for the nullcontrollability of the linear 1d heat equation
(Systems and Control Letters, 20111231)The fact that the heat equation is controllable to zero in any bounded domain of the Euclidean space, any time T>0 and from any open subset of the boundary is well known. On the other hand, numerical experiments show ... 
Best constants and Pohozaev identity for hardysobolevtype operators
(Communications in Contemporary Mathematics, 20131231)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 ... 
Nematic elastomers: Gammalimits for large bodies and small particles
(SIAM Journal on Mathematical Analysis, 20111231)We compute the largebody and the smallparticle Gammalimit of a family of energies for nematic elastomers. We work under the assumption of small deformations (linearized kinematics) and consider both compressible and ... 
Approximation of Hölder continuous homeomorphisms by piecewise affine homeomorphisms
(Houston Journal of Mathematics, 20111231)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 ... 
Stationary policies for the second moment stability in a class of stochastic systems
(Proceedings of the IEEE Conference on Decision and Control, 20111231)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 longrun average cost under a stationary policy is equivalent ... 
Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications
(Journal of the Mechanics and Physics of Solids, 20111231)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
(EPL, 20111231)The fractional Poisson process (FPP) is a counting process with independent and identically distributed interevent times following the MittagLeffler distribution. This process is very useful in several fields of applied ... 
Dispersion for the Schrödinger equation on networks
(Journal of Mathematical Physics, 20111231)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 ... 
The asymptotic behaviour of the heat equation in a twisted DirichletNeumann waveguide
(Journal of Differential Equations, 20111231)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 ... 
Solvability via viscosity solutions for a model of phase transitions driven by configurational forces
(Journal of Differential Equations, 20111231)This article is concerned with an initialboundary value problem for an ellipticparabolic coupled system arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel. This model ... 
Low Mach number limit of viscous polytropic fluid flows
(Journal of Differential Equations, 20111231)This paper studies the singular limit of the nonisentropic NavierStokes equations with zero thermal coefficient in a twodimensional bounded domain as the Mach number goes to zero. A uniform existence result is obtained ... 
A splitting method for the nonlinear Schrödinger equation
(Journal of Differential Equations, 20111231)We introduce a splitting method for the semilinear Schrödinger equation and prove its convergence for those nonlinearities which can be handled by the classical wellposedness L2(Rd)theory. More precisely, we prove that ... 
Wellposedness in critical spaces for the system of compressible NavierStokes in larger spaces
(Journal of Differential Equations, 20111231)This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N≥2. We address the question of wellposedness for large data having critical Besov regularity. Our result improves the analysis ... 
Spherically symmetric solutions to a model for phase transitions driven by configurational forces
(Journal of Mathematical Physics, 20111231)We prove the globalintime existence of spherically symmetric solutions to an initialboundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a ... 
Propagation of chaos in a coagulation model
(Mathematical Models and Methods in Applied Sciences, 20131231)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
(Continuum Mechanics and Thermodynamics, 20111231)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 ... 
A kinetic scheme for transient mixed flows in non uniform closed pipes: A global manner to upwind all the source terms
(Journal of Scientific Computing, 20111231)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 ... 
Homogenization of the Neumann problem in perforated domains: An alternative approach
(Calculus of Variations and Partial Differential Equations, 20111231)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 ...