Exponential Attractors for Parabolic Equations with Dynamic Boundary Conditions

Uniform Exponential Attractors for a Singularly Perturbed Damped Wave Equation

Our aim in this article is to construct exponential attractors for singularly perturbed damped wave equations that are continuous with respect to the perturbation parameter. The main difficulty comes from the fact that the phase spaces for the perturbed and unperturbed equations are not the same; indeed, the limit equation is a (parabolic) reaction-diffusion equation. Therefore, previous constr...

Robust Exponential Attractors for Coleman-gurtin Equations with Dynamic Boundary Conditions Possessing Memory

Well-posedness of generalized Coleman-Gurtin equations equipped with dynamic boundary conditions with memory was recently established by the author with C. G. Gal. In this article we report advances concerning the asymptotic behavior and stability of this heat transfer model. For the model under consideration, we obtain a family of exponential attractors that is robust/Hölder continuous with re...

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

Orbit equivalence of global attractors of semilinear parabolic di erential equations

We consider global attractors Af of dissipative parabolic equations ut = uxx + f(x; u; ux) on the unit interval 0 x 1 with Neumann boundary conditions. A permutation f is de ned by the two orderings of the set of (hyperbolic) equilibrium solutions ut 0 according to their respective values at the two boundary points x = 0 and x = 1: We prove that two global attractors, Af and Ag, are globally C0...

Orbit Equivalence of Global Attractors of Semilinear Parabolic Differential Equations

We consider global attractors Af of dissipative parabolic equations ut = uxx + f(x, u, ux) on the unit interval 0 ≤ x ≤ 1 with Neumann boundary conditions. A permutation πf is defined by the two orderings of the set of (hyperbolic) equilibrium solutions ut ≡ 0 according to their respective values at the two boundary points x = 0 and x = 1. We prove that two global attractors, Af and Ag, are glo...