Global existence and decay of solutions of a singular nonlocal viscoelastic system with damping terms
Nadia Mezouar, Salah Boulaaras
Abstract
In this paper, a singular one-dimensional viscoelastic system with a nonlinear source term, nonlocal boundary condition and damping terms is considered. We prove the existence of a global solution using the potential-well theory. Furthermore, by constructing Lyapunov functional combined with the perturbed energy method, the general decay result is proved.
Topics & Concepts
MathematicsViscoelasticityNonlinear systemTerm (time)Boundary (topology)Mathematical analysisBoundary value problemEnergy functionalLyapunov functionEnergy methodControl theory (sociology)PhysicsControl (management)Computer scienceThermodynamicsArtificial intelligenceQuantum mechanicsStability and Controllability of Differential EquationsAdvanced Mathematical Physics ProblemsNumerical methods in engineering