Semi-discretization in time of a fast diffusion equation

Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model

Full Discretization of the Porous Medium/fast Diffusion Equation Based on Its Very Weak Formulation

Abstract. The very weak formulation of the porous medium/fast diffusion equation yields an evolution problem in a Gelfand triple with the pivot space H. This allows to employ methods of the theory of monotone operators in order to study fully discrete approximations combining a Galerkin method (including conforming finite element methods) with the backward Euler scheme. Convergence is shown eve...

Numerical solution of a fast diffusion equation

In this paper, the authors consider the first boundary value problem for the nonlinear reaction diffusion equation: ut −∆um = αup1 in Ω, a smooth bounded domain in Rd(d ≥ 1) with the zero lateral boundary condition and with a positive initial condition, m ∈ ]0, 1[ (fast diffusion problem), α ≥ 0 and p1 ≥ m. Sufficient conditions on the initial data are obtained for the solution to vanish or bec...

Discretization of Space-time White Noise in the Heat Equation

We consider discretizations of a periodic, one-dimensional spatial white noise. We then propose a particular spectral discretization of space-time white noise and use it to force the heat equation with periodic boundary conditions. We are able to solve explicitly the discretized equations, and then find explicitly the probability distribution of the stationary solution of the heat equation forc...

Semi-discretization in time for Nonlinear Zakharov Waves Equations

In this paper we construct and study discretizations of a nonlinear Zakharov-wave system occurring in plasma physics. These systems are generalizations of the Zakharov system that can be recovered by taking a singular limit. We introduce two numerical schemes that take into account this singular limit process. One of the scheme is conservative but sensible to the polarization of the initial dat...