# Weak exponential attractors for Coleman-Gurtin equations with dynamic boundary conditions possessing different memory kernels

@article{Shomberg2019WeakEA, title={Weak exponential attractors for Coleman-Gurtin equations with dynamic boundary conditions possessing different memory kernels}, author={Joseph L. Shomberg}, journal={Topological Methods in Nonlinear Analysis}, year={2019} }

The well-posedness of a generalized Coleman--Gurtin equation equipped with dynamic boundary conditions with memory was recently established by C.G. Gal and the author. Additionally, it was established by the author that the problem admits a finite dimensional global attractor and a robust family of exponential attractors in the case where singularly perturbed memory kernels defined on the interior of the domain and on the boundary of the domain coincide. In the present article we report…

## References

SHOWING 1-10 OF 39 REFERENCES

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

- Mathematics
- 2016

The well-posedness of a generalized Coleman--Gurtin equation equipped with dynamic boundary conditions with memory was recently established by the author with C.G. Gal. In this article we report…

### Attractors for strongly damped wave equations with nonlinear hyperbolic dynamic boundary conditions

- Mathematics
- 2015

We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter…

### Cahn-Hilliard equations with memory and dynamic boundary conditions

- MathematicsAsymptot. Anal.
- 2011

A modified Cahn-Hiliard equation where the velocity of the order parameter u depends on the past history of Δμ, μ being the chemical potential with an additional viscous term αut, α 0 is considered and existence of a variational solution is obtained.

### Uniform attractors for a non-autonomous semilinear heat equation with memory

- Mathematics
- 2000

In this paper we investigate the asymptotic behavior, as time tends to infinity, of the solutions of an non-autonomous integro-partial differential equation describing the heat flow in a rigid heat…

### The non-isothermal Allen-Cahn equation with dynamic boundary conditions

- Mathematics
- 2008

We consider a model of nonisothermal phase transitions taking
place in a bounded spatial region. The order parameter $\psi$ is governed by
an Allen-Cahn type equation which is coupled with the…

### Asymptotics of the Coleman-Gurtin model

- Mathematics
- 2010

This paper is concerned with the integrodifferential equation $$\partial_t u-\Delta u -\int_0^\infty \kappa(s)\Delta u(t-s)\,\d s + \varphi(u)=f$$ arising in the Coleman-Gurtin's theory of heat…

### Singular limit of viscous Cahn-Hilliard equations with memory and dynamic boundary conditions

- Mathematics
- 2013

We consider a modified Cahn-Hiliard equation
where the velocity of the order parameter $u$ depends on the past
history of $\Delta
\mu $, $\mu $ being the chemical potential with an additional…

### Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions

- MathematicsDifferential and Integral Equations
- 2010

We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as generalizations of semilinear reaction-diffusion equations with dynamic boundary conditions and…

### Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions

- Mathematics
- 2005

We consider in this article the Cahn–Hilliard equation endowed with dynamic boundary conditions. By interpreting these boundary conditions as a parabolic equation on the boundary and by considering a…

### Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary Conditions

- Mathematics
- 2013

Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem…