Existence and uniqueness of local weak solutions for the Emden-Fowler wave equation in one dimension

Abstract

In this article we consider the existence and uniqueness of local weak solutions to the Emden-Fowler type wave equation $$ t^ 2 u_{tt} -u_{{xx}}=|u|^{p-1}u\quad\text{in }[1,T]\times (a,b) $$ with initial-boundary value conditions in a finite time interval.

Keywords

• Emden-Fowler wave equation
• existence
• uniqueness