Stability result of solutions for a Transmition wave equation with internal neutral delay

Abstract

This study examines a wave equation on a bounded domain that incorporates internal neutral delay. By establishing certain conditions, we prove the existence and uniqueness of the solution. Furthermore, we utilize semigroup theory to demonstrate the existence and uniqueness of the problem's solution. Additionally, we employ H. Levine's concavity theorem to establish a time estimate for the explosion of the solutions in Sobolev spaces