Attractors for nonclassical diffusion equations with dynamic boundary conditions. (June 2020) - Lee, Jihoon; Toi, Vu Manh
Abstract: In this paper we study the asymptotic behavior of solutions for a class of nonclassical diffusion equation ∂ t ( u − ε Δ u ) − Δ u + κ u + f ( u ) = g in a smooth bounded domain Ω in R N ( N ≥ 3 ) with dynamic boundary condition ∂ t ( u − ε Δ Γ u ) + ∂ n ( ε ∂ t u + u ) − Δ Γ u + f Γ ( u ) = g Γ on Γ = ∂ Ω . Under a Sobolev type growth condition of the nonlinear functions, we prove the existence and uniqueness of weak solution for the problem by using the Galerkin approximation method, and then establish the existence and upper semicontinuity of global attractors A ε at ε 0 ∈ [ 0, 1 ] by using the asymptotic a priori estimate method.