Blow up of the Solutions of Nonlinear Wave Equation

Abstract

We construct for every fixed the metric , where , , , , are continuous functions, , for which we consider the Cauchy problem , where , ; , , where , , , , , , and are positive constants. When , we prove that the above Cauchy problem has a nontrivial solution in the form for which . When , we prove that the above Cauchy problem has a nontrivial solution in the form for which .