Global existence and exponential decay for a coupled wave system with delay via Kelvin-voigt damping

Resumo

This paper examines the stability of two wave equations coupled through a Kelvin-Voigt damping
mechanism with a time delay in a bounded domain. Using semigroup theory, we establish the global existence
of solutions in an appropriate Sobolev space under suitable conditions. By applying the multiplier method and
Komornik’s integral inequality, we prove an exponential decay rate for the system’s energy. Our results extend
prior work by addressing the combined effects of delay and Kelvin-Voigt damping, providing new insights into
the stabilization of coupled wave systems.