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

Abstract

In this paper, we investigate the long-time behavior of the time-dependent reaction-diffusion equation u_{t}-Δu+a(x)|u|^{ρ}u-b(x)|u|^{ν}u=h(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 W₂¹(Ω)∩L_{ρ+2}(Ω). The existence of a uniform attractor is obtained in W₂¹(Ω)∩L_{ρ+2}(Ω).

Keywords

• Reaction-diffusion equation,Robin boundary value,existence and uniqueness theorems,uniform attractor,process

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