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Abstract: This letter is devoted to results on intermediate asymptotics for the heatequation. We study the convergence towards a stationary solution inself-similar variables. By assuming the equality of some moments of the initialdata and of the stationary solution, we get improved convergence rates usingentropy - entropy-production methods. We establish the equivalence of theexponential decay of the entropies with new, improved functional inequalitiesin restricted classes of functions. This letter is the counterpart in a linearframework of a recent work on fast diffusion equations, seeBonforte-Dolbeault-Grillo-Vazquez. Results extend to the case of aFokker-Planck equation with a general confining potential.



Author: Jean-Philippe Bartier CEREMADE, Adrien Blanchet GREMAQ, Jean Dolbeault CEREMADE, Miguel Escobedo

Source: https://arxiv.org/



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