On the asymptotic positivity of solutions for the extended Fisher–Kolmogorov equation with nonlinear diffusion

✍ Scribed by M. V. Bartuccelli

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 79 KB
• Volume: 25
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.309

✦ Synopsis

Abstract

The objective of this paper aims to prove positivity of solutions for a semilinear dissipative partial differential equation with non‐linear diffusion. The equation is a generalized model of the well‐known Fisher–Kolmogorov equation and represents a class of dissipative partial differential equations containing differential operators of higher order than the Laplacian. It arises in a variety of meaningful physical situations including gas flows, diffusion of an electron–ion plasma and the dynamics of biological populations whose mobility is density dependent. In all these situations, the solutions of the equation must be positive functions. Copyright © 2002 John Wiley & Sons, Ltd.