Inertial manifolds associated to partly dissipative reaction-diffusion systems

Attractors for Partly Dissipative Reaction Diffusion SYstems in R^n

In this paper, we study the asymptotic behavior of solutions for the partly dissipative reaction diffusion equations in ‫ޒ‬ n. We prove the asymptotic compact-ness of the solutions and then establish the existence of the global attractor in 2 Ž n .

Pullback 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.

Partly Dissipative Reaction-diffusion Systems and a Model of Phosphorus Diffusion in Silicon

Upper Semicontinuity of the Attractor for Lattice Dynamical Systems of Partly Dissipative Reaction-diffusion Systems

Lattice dynamical systems arise in various application fields, for instance, in chemical reaction theory, material science, biology, laser systems, image processing and pattern recognition, and electrical engineering (cf. [6, 7, 13]). In each field, they have their own forms, but in some other cases, they appear as spatial discretizations of partial differential equations (PDEs). Recently, many...

Dynamic Optimization of Dissipative PDE Systems Using Approximate Inertial Manifolds

Abstract In this work, we propose a computationally efficient method for the solution of dynamic constraint optimization problems arising in the context of spatiallydistributed processes governed by highly-dissipative nonlinear partial differential equations (PDEs). The method is based on spatial discretization using combination of the method of weighted residuals with spatially-global basis fu...