Robust Stability of Global Attractors for Evolutionary Systems without Uniqueness

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 paper investigates the issue of stability with respect to external disturbances for the global attractor of the wave equation under conditions that do not ensure the uniqueness of the solution to the initial problem. Under general conditions for nonlinear terms, it is proved that the global attractor of the undisturbed problem is locally stable in the sense of ISS and has the AG property with respect to disturbances

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

The paper investigates the issue of stability with respect to external disturbances for the global attractor of the wave equation under conditions that do not ensure the uniqueness of the solution to the initial problem. Under general conditions for nonlinear terms, it is proved that the global attractor of the undisturbed problem is locally stable in the sense of ISS and has the AG property with respect to disturbances