Numerical Solution of a nonlinear reaction-diffusion problem in the case of HS-regime
Provides a numerical approach for a specific class of reaction-diffusion problems, but the result is incremental and domain-specific.
The authors developed a numerical method for a nonlinear reaction-diffusion problem in the HS-regime, proving that the numerical solution blows up in finite time.
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.