Nonexistence of global solutions of abstract wave equations with high energies

We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed analysis whi...

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Autor principal: Esquivel-Avila, Jorge A
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5656739/
https://www.ncbi.nlm.nih.gov/pubmed/29104406
http://dx.doi.org/10.1186/s13660-017-1546-1
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author Esquivel-Avila, Jorge A
author_facet Esquivel-Avila, Jorge A
author_sort Esquivel-Avila, Jorge A
collection PubMed
description We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed analysis which is different from the ones commonly used to prove blow-up. Several examples are given improving known results in the literature.
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spelling pubmed-56567392017-11-01 Nonexistence of global solutions of abstract wave equations with high energies Esquivel-Avila, Jorge A J Inequal Appl Research We consider an undamped second order in time evolution equation. For any positive value of the initial energy, we give sufficient conditions to conclude nonexistence of global solutions. The analysis is based on a differential inequality. The success of our result is based in a detailed analysis which is different from the ones commonly used to prove blow-up. Several examples are given improving known results in the literature. Springer International Publishing 2017-10-25 2017 /pmc/articles/PMC5656739/ /pubmed/29104406 http://dx.doi.org/10.1186/s13660-017-1546-1 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
Esquivel-Avila, Jorge A
Nonexistence of global solutions of abstract wave equations with high energies
title Nonexistence of global solutions of abstract wave equations with high energies
title_full Nonexistence of global solutions of abstract wave equations with high energies
title_fullStr Nonexistence of global solutions of abstract wave equations with high energies
title_full_unstemmed Nonexistence of global solutions of abstract wave equations with high energies
title_short Nonexistence of global solutions of abstract wave equations with high energies
title_sort nonexistence of global solutions of abstract wave equations with high energies
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5656739/
https://www.ncbi.nlm.nih.gov/pubmed/29104406
http://dx.doi.org/10.1186/s13660-017-1546-1
work_keys_str_mv AT esquivelavilajorgea nonexistenceofglobalsolutionsofabstractwaveequationswithhighenergies

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