Numerical Solution of a nonlinear reaction-diffusion problem in the case of HS-regime

Details Numerical Solution of a nonlinear reaction-diffusion problem in the case of HS-regime Numerical Solution of a nonlinear reaction-diffusion problem in the case of HS-regime

2009-05-18

arxiv.org/abs/0905.2861v1

Mathematics

Numerical Analysis

14 pages

Scientific paper

In this paper, the authors propose a numerical method to compute the solution of a nonlinear reaction-diffusion problem in the case of HS-regime. The initial condition is a nonnegative function with compact support. The problem is split in two parts: A hyperbolic term solved by using the Hopf and Lax formula and a parabolic term solved by a backward linearized Euler method in time and a finite element method in space. Estimates of the numerical solution are obtained and it is proved that any numerical solution blows up in finite time.

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