| Abstract: |
| We consider a class of second order evolution equations in time. In order to show the non existence of global solutions with high values of the initial energy, we analyze a differential inequality and present a positive invariant set for this purpose. On the other hand, the study of global solutions for high initial values of energy seems not to be a simple problem. We discussed the feasibility of the existence of a new invariant recently proposed in the literature. Our talk is based in the following papers.
\begin{itemize}
\item {\sc Esquivel-Avila, Jorge A.}, A differential inequality and the blow-up of its solutions, {\it Applied Mathematics E-Notes}, Vol 22, 2022, 178-183. https://www.emis.de/journals/AMEN/
\item {\sc Esquivel-Avila, Jorge A.}, On the Global Solutions of Abstract Wave Equations with High Energies, {\it Mathematical Notes}, Vol 11, No 4, 2022, 525-533. https://link.springer.com/article/10.1134/S0001434622030208
\end{itemize} |
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