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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Detalles Bibliográficos
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
Descripción
Sumario: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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