Premium
On the asymptotic positivity of solutions for the extended Fisher–Kolmogorov equation with nonlinear diffusion
Author(s) -
Bartuccelli M. V.
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.309
Subject(s) - mathematics , dissipative system , partial differential equation , first order partial differential equation , nonlinear system , differential equation , mathematical analysis , fisher's equation , diffusion equation , diffusion , fisher equation , laplace operator , exact differential equation , physics , economy , real interest rate , quantum mechanics , monetary economics , economics , thermodynamics , interest rate , service (business)
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.