Entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity

This paper is concerned with the existence of entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity. Here the entire solutions are the classical solutions that exist for all [Formula: see text] . With the aid of the comparison theorem and the sup-sub solutions method...

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Detalles Bibliográficos
Autores principales: Yan, Rui, Li, Xiaocui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5915528/
https://www.ncbi.nlm.nih.gov/pubmed/29721008
http://dx.doi.org/10.1186/s13662-018-1606-y
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author Yan, Rui
Li, Xiaocui
author_facet Yan, Rui
Li, Xiaocui
author_sort Yan, Rui
collection PubMed
description This paper is concerned with the existence of entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity. Here the entire solutions are the classical solutions that exist for all [Formula: see text] . With the aid of the comparison theorem and the sup-sub solutions method, we construct some entire solutions that behave as two opposite traveling front solutions with critical speeds moving towards each other from both sides of x-axis and then annihilating. In addition, we apply the existence theorem to a specially doubly degenerate case.
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spelling pubmed-59155282018-04-30 Entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity Yan, Rui Li, Xiaocui Adv Differ Equ Research This paper is concerned with the existence of entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity. Here the entire solutions are the classical solutions that exist for all [Formula: see text] . With the aid of the comparison theorem and the sup-sub solutions method, we construct some entire solutions that behave as two opposite traveling front solutions with critical speeds moving towards each other from both sides of x-axis and then annihilating. In addition, we apply the existence theorem to a specially doubly degenerate case. Springer International Publishing 2018-04-24 2018 /pmc/articles/PMC5915528/ /pubmed/29721008 http://dx.doi.org/10.1186/s13662-018-1606-y Text en © The Author(s) 2018 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
Yan, Rui
Li, Xiaocui
Entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity
title Entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity
title_full Entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity
title_fullStr Entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity
title_full_unstemmed Entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity
title_short Entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity
title_sort entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5915528/
https://www.ncbi.nlm.nih.gov/pubmed/29721008
http://dx.doi.org/10.1186/s13662-018-1606-y
work_keys_str_mv AT yanrui entiresolutionsforareactiondiffusionequationwithdoublydegeneratenonlinearity
AT lixiaocui entiresolutionsforareactiondiffusionequationwithdoublydegeneratenonlinearity

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