Global Attractors and Asymptotic Gain Property for Non-Autonomous Inclusion of Reaction–Diffusion Type

Abstract

We investigate global resolvability and stability of attractors for parabolic inclusion with multi-valued interaction function of reaction-diffusion type and non-autonomous disturbances. For the class of L2-disturbances, we prove existence of global solutions in the phase space L2. In the class of translation-bounded disturbances we prove that obtained global solutions generate the family of multi-valued semiprocesses which possesses a uniform attractor. Finally, for L∞-disturbances we show that the global attractor of unperturbed system is stable w.r.t. disturbances in the asymptotic gain sense.

Keywords

• parabolic inclusion
• reaction-diffusion
• uniform attractor
• stability
• asymptotic gain