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On the problem of asymptotic positivity of solutions for dissipative partial differential equations
1Department of Mathematics and Statistics, University of Surrey, Guildford, GU2 5XH England.
Abstract:
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.
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