Stability and asymptotic properties of dissipative evolution equations coupled with ordinary differential equations

Abstract

<p style='text-indent:20px;'>In this paper, we obtain some stability results of systems corresponding to the coupling between a dissipative evolution equation (set in an infinite dimensional space) and an ordinary differential equation. Many problems from physics enter in this framework, let us mention dispersive medium models, generalized telegraph equations, Volterra integro-differential equations, and cascades of ODE-hyperbolic systems. The goal is to find sufficient (and necessary) conditions on the involved operators that garantee stability properties of the system, i.e., strong stability, exponential stability or polynomial one. We also illustrate our abstract statements for different concrete examples, where new results are achieved.</p>