Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential
نویسندگان
چکیده
A reaction-diffusion problem with an obstacle potential is considered in a bounded domain of R . Under the assumption that the obstacle K is a closed convex and bounded subset of R with smooth boundary or it is a closed n-dimensional simplex, we prove that the long-time behavior of the solution semigroup associated with this problem can be described in terms of an exponential attractor. In particular, the latter means that the fractal dimension of the associated global attractor is also finite.
منابع مشابه
Modelling the catalyst fragmentation pattern in relation to molecular properties and particle overheating in olefin polymerization
A two-dimensional single particle finite element model was used to examine the effects of particle fragmental pattern on the average molecular weights, polymerization rate and particle overheating in heterogeneous Ziegler-Natta olefin polymerization. A two-site catalyst kinetic mechanism was employed together with a dynamic two-dimensional molecular species in diffusion-reaction equation. The i...
متن کاملPullback D-attractors for non-autonomous partly dissipative reaction-diffusion equations in unbounded domains
At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.
متن کاملElasto-Thermodiffusive Response in a Two-Dimensional Transversely Isotropic Medium
The present article investigates the elasto-thermodiffusive interactions in a transversely isotropic elastic medium in the context of thermoelasticity with one relaxation time parameter and two relation time parameters. The resulting non-dimensional coupled equations are applied to a specific problem of a half-space in which the surface is free of tractions and is subjected to time-dependent th...
متن کاملA Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method
In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...
متن کاملFinite Element Methods for Convection Diffusion Equation
This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...
متن کامل