Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem
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Título: | Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem |
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Autor/es: | Esteve, Carlos | Rossi, Julio D. | San Antolín Gil, Ángel |
Grupo/s de investigación o GITE: | Curvas Alpha-Densas. Análisis y Geometría Local |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Análisis Matemático |
Palabras clave: | Nonlocal diffusion | Decay rates |
Área/s de conocimiento: | Análisis Matemático |
Fecha de publicación: | 13-may-2014 |
Editor: | Springer |
Cita bibliográfica: | Boundary Value Problems 2014, 2014:109. doi:10.1186/1687-2770-2014-109 |
Resumen: | We obtain upper bounds for the decay rate for solutions to the nonlocal problem ∂tu(x,t)=∫RnJ(x,y)|u(y,t)−u(x,t)|p−2(u(y,t)−u(x,t))dy with an initial condition u0∈L1(Rn)∩L∞(Rn) and a fixed p>2. We assume that the kernel J is symmetric, bounded (and therefore there is no regularizing effect) but with polynomial tails, that is, we assume a lower bounds of the form J(x,y)≥c1|x−y|−(n+2σ), for |x−y|>c2 and J(x,y)≥c1, for |x−y|≤c2. We prove that ∥u(⋅,t)∥Lq(Rn)≤Ct−n(p−2)n+2σ(1−1q) for q≥1 and t large. |
Patrocinador/es: | This work was partially supported by MEC MTM2010-18128 and MTM2011-27998 (Spain). |
URI: | http://hdl.handle.net/10045/43966 |
ISSN: | 1687-2762 (Print) | 1687-2770 (Online) |
DOI: | 10.1186/1687-2770-2014-109 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2014 Esteve et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. |
Revisión científica: | si |
Versión del editor: | http://dx.doi.org/10.1186/1687-2770-2014-109 |
Aparece en las colecciones: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
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