Pullback Attractors for the Non-autonomous FitzHugh-Nagumo System on Unbounded Domains
نویسنده
چکیده
The existence of a pullback attractor is established for the singularly perturbed FitzHughNagumo system defined on the entire space Rn when external terms are unbounded in a phase space. The pullback asymptotic compactness of the system is proved by using uniform a priori estimates for far-field values of solutions. Although the limiting system has no global attractor, we show that the pullback attractors for the perturbed system with bounded external terms are uniformly bounded, and hence do not blow up as a small parameter approaches zero.
منابع مشابه
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.
متن کاملRandom Attractors for the Stochastic FitzHugh-Nagumo System on Unbounded Domains
The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.
متن کاملPullback Attractors for Reaction-diffusion Equations in Some Unbounded Domains with an H-valued Non-autonomous Forcing Term and without Uniqueness of Solutions
The existence of a pullback attractor for a reaction-diffusion equations in an unbounded domain containing a non-autonomous forcing term taking values in the space H, and with a continuous nonlinearity which does not ensure uniqueness of solutions, is proved in this paper. The theory of set-valued non-autonomous dynamical systems is applied to the problem. Dedicated to Peter E. Kloeden on his 6...
متن کاملPeriodic Random Attractors for Stochastic Navier-stokes Equations on Unbounded Domains
This article concerns the asymptotic behavior of solutions to the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. First we introduce a continuous cocycle for the equations and then prove the existence and uniqueness of tempered random attractors. We also characterize the structures of the random attractors by comp...
متن کاملPullback attractors for non-autonomous reaction-diffusion equations in Lp
We study the long time behavior of solutions of the non-autonomous Reaction-Diffusion equation defined on the entire space Rn when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L(R) and H(R), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of...
متن کامل