Pullback Exponential Attractors for Parabolic Equations with Dynamical Boundary Conditions

Exponential Attractors for Parabolic Equations with Dynamic Boundary Conditions

We study exponential attractors for semilinear parabolic equations with dynamic boundary conditions in bounded domains. First, we give the existence of the exponential attractor in L2(Ω) × L2(Γ) by proving that the corresponding semigroup satisfies the enhanced flattering property. Second, we apply asymptotic a priori estimate and obtain the exponential attractor in Lp(Ω) × L(Γ). Finally, we sh...

Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator

and Applied Analysis 3 The content of the paper is as follows. In Section 2, for the convenience of the reader, we recall some concepts and results on function spaces and pullback attractors which we will use. In Section 3, we prove the existence of pullback attractors in the spaces S0 Ω and L2p−2 Ω by using the asymptotic a priori estimate method. In Section 4, under additional assumptions of ...

Pullback Attractors for Non-autonomous Parabolic Equations Involving Grushin Operators

Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain. We assume a polynomial type growth on the nonlinearity, and an exponential growth on the external force. The obtained results extend some existing results for non-autonomous reaction-diffusi...

Pullback Exponential Attractors for Nonautonomous Reaction-Diffusion Equations

Under the assumption that g t ( ) is translation bounded in loc L R L 4 4 ( ; ( )) Ω , and using the method developed in [3], we prove the existence of pullback exponential attractors in H 1 0 ( ) Ω for nonlinear reaction diffusion equation with polynomial growth nonlinearity( p 2 ≥ is arbitrary).

Attractors for Parabolic Equations with Nonlinear Boundary Conditions, Critical Exponents, and Singular Initial Data