Differential inequalities of parabolic type in the Sobolev space
Diffusion and cross-diffusion in pattern formation
We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.
Diffusion models and their accelerated solution in image and surface processing.
Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions
The paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. General nonconforming meshes are used and the NIPG, IIPG and SIPG versions of the discretization of diffusion terms are considered. The main attention is paid to the impact of the Neumann boundary condition prescribed on a part of the boundary on the truncation...
Domains of attraction of equilibria and monotonicity properties of convergent trajectories in parabolic systems admitting strong comparison principle.
Double-barriers-reflected BSDEs with jumps and viscosity solutions of parabolic integrodifferential PDEs.
Droplet spreading under weak slippage : the waiting time phenomenon
Dynamic programming for stochastic target problems and geometric flows
Dynamique des tourbillons de vorticité pour l’équation de Ginzburg-Landau parabolique
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.