Well-posedness and exponential stability for the logarithmic Lamé system with a time delay
Hazal Yüksekkaya, Erhan Pışkın, Mohammad Kafini, Adel M. Al‐Mahdi
Abstract
This paper is concerned with the initial-boundary value problem for a logarithmic Lamé system with a time delay in a bounded domain. We prove the well-posedness of the system by utilizing the semigroup theory. Then, we prove the existence of global solutions by using the well-depth method. In addition, we establish an exponential stability decay result under appropriate assumptions on the weight of the time delay and that of frictional damping.
Topics & Concepts
MathematicsSemigroupLogarithmExponential stabilityBounded functionExponential decayDomain (mathematical analysis)Exponential functionMathematical analysisExponential growthStability (learning theory)Initial value problemApplied mathematicsControl theory (sociology)Nonlinear systemComputer scienceControl (management)Machine learningQuantum mechanicsNuclear physicsArtificial intelligencePhysicsStability and Controllability of Differential EquationsAdvanced Mathematical Physics ProblemsAdvanced Mathematical Modeling in Engineering