Asymptotic Behavior of the Non-Autonomous Reaction-Diffusion Equation with Robin Boundary Condition

Authors : Eylem ÖZTÜRK

Pages : 422-440

Doi:10.31801/cfsuasmas.425500

View : 14 | Download : 11

Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :In this paper, we investigate the long-time behavior of the time-dependent reaction-diffusion equation u_{t}-Δu+ainsert ignore into journalissuearticles values(x);|u|^{ρ}u-binsert ignore into journalissuearticles values(x);|u|^{ν}u=hinsert ignore into journalissuearticles values(x,t); with Robin boundary condition. We begin this paper with the existence and uniqueness results of the solution to the problem. For the asymptotic behavior, we firstly prove the existence of an absorbing set in W₂¹insert ignore into journalissuearticles values(Ω);∩L_{ρ+2}insert ignore into journalissuearticles values(Ω);. The existence of a uniform attractor is obtained in W₂¹insert ignore into journalissuearticles values(Ω);∩L_{ρ+2}insert ignore into journalissuearticles values(Ω);.
Keywords : Reaction diffusion equation, Robin boundary value, existence and uniqueness theorems, uniform attractor, process