Home > Books and collections > Book chapters > Analysis and numerical approximation of viscosity solutions with shocks : |
Date: | 2011 |
Abstract: | We consider a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion function that depends on the unknown and on the gradient of the unknown. The new class of Hamilton-Jacobi equations represents the propagation of fronts with speed that is a nonlinear function of the signal. The equations contain a nonstandard Hamiltonian that allows the presence of shocks in the solution and these shocks propagate with nonlinear velocity. We focus on the one-dimensional plasma equation as an example of the general Fokker-Planck equations having the features we are interested in analyzing. We explore features of the solution of the corresponding Hamilton-Jacobi plasma equation and propose a suitable fifth order finite difference numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We present numerical results performed under different initial data with compact support. |
Grants: | Ministerio de Ciencia e Innovación MTM2008-03597 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Capítol de llibre ; recerca ; Versió acceptada per publicar |
Subject: | Fokker-Planck equation ; Hamilton-Jacobi equations ; Plasma equation ; Numerical schemes |
Published in: | Advances in Mathematical and Computational Methods: addressing modern challenges of science, technology, and society, 2011, p. 41-44 |
Postprint 4 p, 132.0 KB |