On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass
We extend the existing theory on large-time asymptotics for convection-diffusion equations, based on the entropy-entropy dissipation approach, to certain fast diffusion equations with uniformly convex confinement potential and finite-mass but infinite-entropy equilibrium solutions. We prove existenc...
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| Autores principales: | , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03605302_v28_n1-2_p301_Lederman |
| Aporte de: |
| Sumario: | We extend the existing theory on large-time asymptotics for convection-diffusion equations, based on the entropy-entropy dissipation approach, to certain fast diffusion equations with uniformly convex confinement potential and finite-mass but infinite-entropy equilibrium solutions. We prove existence of a mass preserving solution of the Cauchy problem and we show exponential convergence, as t → ∞, at a precise rate to the corresponding equilibrium solution in the L1 norm. As by-product we also derive corresponding generalized Sobolev inequalities. |
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