A sufficient condition for global existence of the solution to nonlinear damped wave equations at arbitrary positive initial energy

Abstract

AbstractWe consider the global existence of the solution for nonlinear damped wave equations at arbitrary positive initial energy, that is, . It is well known from a work of G. Filippo and S. Marco [Ann. Inst. H. Poincaré Anal. Non Linéaire, 2006], that which initial data with high energy make the model exists global solutions is still an interesting question. Here, we give it an affirmative answer. For this purpose, we suggest a unified approach, which is also valid where various forms of damping are present. Applying it, we show a sufficient condition to get the global existence of the solution for problem nonlinear damped wave equations.