1. Improved intermediate asymptotics for the heat equation
- Author
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Bartier, Jean-Philippe, Blanchet, Adrien, Dolbeault, Jean, and Escobedo, Miguel
- Subjects
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ASYMPTOTIC theory in partial differential equations , *HEAT equation , *STOCHASTIC convergence , *SELF-similar processes , *FUNCTIONAL analysis , *MATHEMATICAL inequalities , *FOKKER-Planck equation - Abstract
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) . The results extend to the case of a Fokker–Planck equation with a general confining potential. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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