Remark on the Cauchy problem for the evolution p-Laplacian equation

In this paper, we prove that the semigroup [Formula: see text] generated by the Cauchy problem of the evolution p-Laplacian equation [Formula: see text] ([Formula: see text] ) is continuous form a weighted [Formula: see text] space to the continuous space [Formula: see text] . Then we use this prope...

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Detalles Bibliográficos
Autores principales: Wang, Liangwei, Yin, Jngxue, Cao, Jinde
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5556400/
https://www.ncbi.nlm.nih.gov/pubmed/28855784
http://dx.doi.org/10.1186/s13660-017-1449-1
Descripción
Sumario:In this paper, we prove that the semigroup [Formula: see text] generated by the Cauchy problem of the evolution p-Laplacian equation [Formula: see text] ([Formula: see text] ) is continuous form a weighted [Formula: see text] space to the continuous space [Formula: see text] . Then we use this property to reveal the fact that the evolution p-Laplacian equation generates a chaotic dynamical system on some compact subsets of [Formula: see text] . For this purpose, we need to establish the propagation estimates and the space-time decay estimates for the solutions first.

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