On behavior of solutions to a class of nonlinear hyperbolic inverse source problem

Abstract

This article is concerned with a class of hyperbolic inverse source problem with memory term and nonlinear boundary damping. Under appropriate assumptions on the initial data and parameters in the equation, we establish two results on behavior of solutions. At first we proved stability of solutions when the integral overdetermination tends to zero as time goes to infinity and finally a blow-up result is established for certain solution with positive initial energy.