Écoulements en milieu poreux n'obéissant pas à la loi de Darcy
EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires
Effets régularisants de semi-groupes non linéaires dans des espaces de Banach
Efficient algorithm to solve optimal boundary control problem for Burgers' equation
In this paper, we propose a novel algorithm for solving an optimal boundary control problem of the Burgers' equation. The solving method is based on the transformation of the original problem into a homogeneous boundary conditions problem. This transforms the original problem into an optimal distributed control problem. The modal expansion technique is applied to the distributed control problem of the Burgers' equation to generate a low-dimensional dynamical system. The control parametrization method...
Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
In this paper, we extend the reduced-basis approximations developed earlier for linear elliptic and parabolic partial differential equations with affine parameter dependence to problems involving (a) nonaffine dependence on the parameter, and (b) nonlinear dependence on the field variable. The method replaces the nonaffine and nonlinear terms with a coefficient function approximation which then permits an efficient offline-online computational decomposition. We first review the coefficient function...
Ein Maximumprinzip für nichtlineare parabolische Systeme.
Eine parabolische Gleichung mit vergänglichen Lösungen.
Elliptic regularization and Navier-Stokes system.
Entropy solution for anisotropic reaction-diffusion-advection systems with L1 data.
In this paper, we study the question of existence and uniqueness of entropy solutions for a system of nonlinear partial differential equations with general anisotropic diffusivity and transport effects, supplemented with no-flux boundary conditions, modeling the spread of an epidemic disease through a heterogeneous habitat.
Entropy solutions for parabolic equations in Musielak framework without sign condition and with measure data
We prove an existence result of entropy solutions for a class of strongly nonlinear parabolic problems in Musielak-Sobolev spaces, without using the sign condition on the nonlinearities and with measure data.
Entropy solutions to a second order forward-backward parabolic differential equation.
Équations aux dérivées partielles stochastiques de type monotone
Équations d'évolution paraboliques fortement non linéaires
Équations différentielles ordinaires et équations de transport avec des coefficients irréguliers
Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes
We consider the lowest-order Raviart–Thomas mixed finite element method for second-order elliptic problems on simplicial meshes in two and three space dimensions. This method produces saddle-point problems for scalar and flux unknowns. We show how to easily and locally eliminate the flux unknowns, which implies the equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. The matrix of the final linear system is sparse, positive...
Erratum: A Parabolic Quasilinear Problem for Linear Growth Functionals.
Error estimates for Euler forward scheme related to two-phase Stefan problems
Error estimates for finite element methods for semilinear parabolic problems with nonsmooth data
Error estimates for finite volume scheme for Perona--Malik equation.
Error estimates of a fully discrete linear approximation scheme for Stefan problem.