Robust Stability of Global Attractors for Evolutionary Systems without Uniqueness

Abstract

We establish the local input-to-state stability of multi-valued evolutionary systems with bounded disturbances with respect to the global attractor of the respective undisturbed system. We apply obtained results to disturbed reaction-diffusion equation.

Stability w.r.t. Disturbances for the Global Attractor of Multi-Valued Semiflow Generated by Nonlinear Wave Equation

“…The corresponding technique was developed in the works of [14,15] and applied to the wave equation with a smooth interaction function f and disturbances of the type h(x)d(t) in the work [16]. The extension of this theory to the case of non-uniqueness of solution of the initial problem was carried out in [17], where the local ISS property of the attractor was established for the reaction-diffusion system.…”