General decay for a viscoelastic von Karman equation with delay and variable exponent nonlinearities
Sun‐Hye Park
Abstract
Abstract In this paper, we consider a viscoelastic von Karman equation with damping, delay, and source effects of variable exponent type. Firstly, we show the global existence of solution applying the potential well method. Then, by making use of the perturbed energy method and properties of convex functions, we derive general decay results for the solution under more general conditions of a relaxation function. General decay results of solutions for viscoelastic von Karman equations with variable exponent nonlinearities have not been discussed before. Our results extend and complement many results for von Karman equations in the literature.
Topics & Concepts
ViscoelasticityMathematicsExponentMathematical analysisRelaxation (psychology)Variable (mathematics)Bounded functionPhysicsThermodynamicsPsychologySocial psychologyPhilosophyLinguisticsStability and Controllability of Differential EquationsAdvanced Mathematical Physics ProblemsNumerical methods for differential equations