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Pullback attractors for non-autonomous quasi-linear parabolic equations with dynamical boundary conditions. (English) Zbl 1261.37033

The authors consider the following non-autonomous quasi-linear parabolic equation

u t -div(|u| p-2 u)+f(u)=h(t),inΩ,

with the dynamical boundary condition

u t +|u| p-2 n u+g(u)=0,onΓ

and the initial condition

u(τ)=u τ ,inΩ ¯,

where Ω is a bounded domain of N with smooth boundary Γ, p2, h,f,g satisfy some conditions.

By the theory of pullback attractors, the authors analyze the asymptotic behavior of the solutions of the problem.

37L05General theory, nonlinear semigroups, evolution equations
35B40Asymptotic behavior of solutions of PDE
35B41Attractors (PDE)