Existence and energy decay rate of the solutions for the wave equation with a nonlinear distributed delay

Abstract

<abstract><p>This paper is concerned with the wave equation having a nonlinear distributed delay. First, we prove the local existence of the solutions by using the semigroup theory, where the source term is globally Lipschitz. Next, we establish the global existence of solutions and the energy decay result under the local Lipschitz source and suitable conditions on the initial data.</p></abstract>