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...

Descripción completa

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
_version_ 1783257057916354560
author Wang, Liangwei
Yin, Jngxue
Cao, Jinde
author_facet Wang, Liangwei
Yin, Jngxue
Cao, Jinde
author_sort Wang, Liangwei
collection PubMed
description 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.
format Online
Article
Text
id pubmed-5556400
institution National Center for Biotechnology Information
language English
publishDate 2017
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-55564002017-08-28 Remark on the Cauchy problem for the evolution p-Laplacian equation Wang, Liangwei Yin, Jngxue Cao, Jinde J Inequal Appl Research 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. Springer International Publishing 2017-08-01 2017 /pmc/articles/PMC5556400/ /pubmed/28855784 http://dx.doi.org/10.1186/s13660-017-1449-1 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Wang, Liangwei
Yin, Jngxue
Cao, Jinde
Remark on the Cauchy problem for the evolution p-Laplacian equation
title Remark on the Cauchy problem for the evolution p-Laplacian equation
title_full Remark on the Cauchy problem for the evolution p-Laplacian equation
title_fullStr Remark on the Cauchy problem for the evolution p-Laplacian equation
title_full_unstemmed Remark on the Cauchy problem for the evolution p-Laplacian equation
title_short Remark on the Cauchy problem for the evolution p-Laplacian equation
title_sort remark on the cauchy problem for the evolution p-laplacian equation
topic Research
url 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
work_keys_str_mv AT wangliangwei remarkonthecauchyproblemfortheevolutionplaplacianequation
AT yinjngxue remarkonthecauchyproblemfortheevolutionplaplacianequation
AT caojinde remarkonthecauchyproblemfortheevolutionplaplacianequation

Ejemplares similares