Nonexistence of global solutions of abstract wave equations with high energies

Abstract

Abstract 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.

Keywords

• abstract wave equation
• nonexistence
• blow up
• global solutions
• high energies