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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03605302_v28_n1-2_p301_Lederman |
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todo:paper_03605302_v28_n1-2_p301_Lederman2023-10-03T15:26:36Z On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass Lederman, C. Markowich, P.A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03605302_v28_n1-2_p301_Lederman |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| format |
JOUR |
| author |
Lederman, C. Markowich, P.A. |
| spellingShingle |
Lederman, C. Markowich, P.A. On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass |
| author_facet |
Lederman, C. Markowich, P.A. |
| author_sort |
Lederman, C. |
| title |
On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass |
| title_short |
On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass |
| title_full |
On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass |
| title_fullStr |
On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass |
| title_full_unstemmed |
On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass |
| title_sort |
on fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass |
| url |
http://hdl.handle.net/20.500.12110/paper_03605302_v28_n1-2_p301_Lederman |
| work_keys_str_mv |
AT ledermanc onfastdiffusionequationswithinfiniteequilibriumentropyandfiniteequilibriummass AT markowichpa onfastdiffusionequationswithinfiniteequilibriumentropyandfiniteequilibriummass |
| _version_ |
1807317135230238720 |