Toscani, G. Kinetic approach to the asymptotic behaviour of the solution to diffusion equations. (English) Zbl 0904.35029 Rend. Mat. Appl., VII. Ser. 16, No. 2, 329-346 (1996). 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) Cited in 7 Documents MSC: 35K05 Heat equation 35B40 Asymptotic behavior of solutions to PDEs 35K10 Second-order parabolic equations Keywords:logarithmic Sobolev inequality; central limit theorem; relative entropy PDFBibTeX XMLCite \textit{G. Toscani}, Rend. Mat. Appl., VII. Ser. 16, No. 2, 329--346 (1996; Zbl 0904.35029)