Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1708779 | Applied Mathematics Letters | 2011 | 6 Pages |
Abstract
This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the stationary solution, we get improved convergence rates using entropy/entropy-production methods. We establish the equivalence of the exponential decay of the entropies with new, improved functional inequalities in restricted classes of functions. This letter is the counterpart in a linear framework of a recent work on fast diffusion equations; see Bonforte et al. (2009) [18]. The results extend to the case of a Fokker–Planck equation with a general confining potential.
Related Topics
Physical Sciences and Engineering
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Authors
Jean-Philippe Bartier, Adrien Blanchet, Jean Dolbeault, Miguel Escobedo,