Asymptotic behavior of a viscoelastic wave equation with a delay in internal fractional feedback
Radhouane Aounallah, Adbelbaki Choucha, Salah Boulaaras, Abderrahmane Zaraï
Abstract
We consider the viscoelastic wave equation with a time delay term in internal fractional feedback. By employing the energy method along with the Faedo-Galerkin procedure, we establish the global existence of solutions, subject to certain conditions. Additionally, we demonstrate how appropriate Lyapunov functionals can lead to general decay results of the energy.
Topics & Concepts
ViscoelasticityControl theory (sociology)Mathematical analysisMathematicsInternal modelPhysicsComputer scienceThermodynamicsArtificial intelligenceControl (management)Stability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringFractional Differential Equations Solutions