Existence and Asymptotic Behavior of Solutions for some Hyperbolic Systems

Abstract

In this research, we examined the existence and asymptotic behavior of solutions for a BresseTimoshenko system, considering distributed delay and second sound effects. In a section of this study,we demonstrated the global well-posedness of the initial and boundary value problem, given appropriate assumptions, utilizing Faedo-Galarkin approximations and several energy estimates. In the final section, exponential stability was demonstrated through the utilization of Lyapunov functional and the multiplier technic.