Existence, Nonexistence, and Stability of Solutions for a Delayed Plate Equation with the Logarithmic Source
Hazal Yüksekkaya, Erhan Pışkın, Salah Boulaaras, Bahri Cherif, Sulima Ahmed Zubair
Abstract
In this work, we study a plate equation with time delay in the velocity, frictional damping, and logarithmic source term. Firstly, we obtain the local and global existence of solutions by the logarithmic Sobolev inequality and the Faedo-Galerkin method. Moreover, we prove the stability and nonexistence results by the perturbed energy and potential well methods.
Topics & Concepts
LogarithmMathematicsStability (learning theory)Mathematical analysisWork (physics)Sobolev spaceLogarithmic decrementApplied mathematicsPhysicsComputer scienceThermodynamicsMachine learningQuantum mechanicsVibrationStability and Controllability of Differential EquationsAdvanced Mathematical Physics ProblemsAdvanced Mathematical Modeling in Engineering