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Kinetic approach to the asymptotic behaviour of the solution to diffusion equations. (English) Zbl 0904.35029

In the first part of this paper, the asymptotic behaviour, for \(t\to\infty\), of solutions of the heat equation is investigated. For initial values with certain properties the author gives estimates for the relative entropy of the solution with respect to a suitably time translated fundamental solution of the heat equation. The method is then applied to study the asymptotic behaviour of solutions of a class of uniformly parabolic equations.
Reviewer: J.Voigt (Dresden)

MSC:

35K05 Heat equation
35B40 Asymptotic behavior of solutions to PDEs
35K10 Second-order parabolic equations
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