Improved intermediate asymptotics for the heat equation

2009/08/16 by Jean-Philippe Bartier, Adrien Blanchet, Bartier, Jean-Philippe +5
Mathematics · Physics and Astronomy · #26D10 #35K10 #35K15 #47J20 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #msc:26D10 #msc:35K10 #msc:35K15 #msc:47J20

paper · pdf · doi:10.48550/arxiv.0908.2226

arxiv created 2009/08/16 · openalex publication_date 2009/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-Dolbeault-Grillo-Vazquez]. Results extend to the case of a Fokker-Planck equation with a general confining potential.

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