GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A LOGARITHMIC WAVE EQUATION ARISING FROM Q-BALL DYNAMICS

Abstract

In this paper we investigate an initial boundary value prob- lem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem. In this paper we study the global existence of weak solutions for the initial boundary value problem 8 utt − �u + u − ulogjuj 2 + ut + juj 2 u = 0, (x,t) 2 � (0,T), u = 0, (x,t) 2 @ � (0,T), u(x,0) = u 0 (x), ut(x,0) = u 1 (x), x 2 ,