On the problem of asymptotic positivity of solutions for dissipative partial differential equations.
The objective of this paper aims to prove positivity of solutions for the following semilinear partial differential equationu[Formula: see text]. This equation represents a generalised model of the so-called porous medium equation. 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.
Department of Mathematics and Statistics, University of Surrey, Guildford, GU2 5XH England.
M V
MV
Bartuccelli
S A
SA
Gourley
Dissipative partial differential equations; Interpolationinequalities; Ladder methods; Positivity