اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPullback Attractors for the Non-autonomous FitzHugh-Nagumo System on Unbounded Domains
207
0
0.0
(
0
)
تأليف
Bixiang Wang
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The existence of a pullback attractor is established for the singularly perturbed FitzHugh-Nagumo system defined on the entire space $R^n$ 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.
قيم البحث
اقرأ أيضاً
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.
This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space R^n. We first establish the asymptotic compactness of the equation in L^2(R^n) and then prove the existence and uniqueness of non-autono
mous random attractors. This attractor is pathwise periodic if the non-autonomous deterministic forcing is time periodic. The difficulty of non-compactness of Sobolev embeddings on R^n is overcome by the uniform smallness of solutions outside a bounded domain.
We study the long time behavior of solutions of the non-autonomous Reaction-Diffusion equation defined on the entire space R^n when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is establ
ished in L^2(R^n) and H^1(R^n), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of solutions outside bounded domains.
In this article we study the asymptotic behavior of solutions, in sense of global pullback attractors, of the evolution system $$ begin{cases} u_{tt} +etaDelta^2 u+a(t)Deltatheta=f(t,u), & t>tau, xinOmega, theta_t-kappaDelta theta-a(t)Delta u_t=0, &
t>tau, xinOmega, end{cases} $$ subject to boundary conditions $$ u=Delta u=theta=0, t>tau, xinpartialOmega, $$ where $Omega$ is a bounded domain in $mathbb{R}^N$ with $Ngeqslant 2$, which boundary $partialOmega$ is assumed to be a $mathcal{C}^4$-hypersurface, $eta>0$ and $kappa>0$ are constants, $a$ is an Holder continuous function, $f$ is a dissipative nonlinearity locally Lipschitz in the second variable.
This paper is concerned with the asymptotic behavior of solutions of the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. We first 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 complete solutions. When deterministic forcing terms are periodic, we show that the tempered random attractors are also periodic. Since the Sobolev embeddings on unbounded domains are not compact, we establish the pullback asymptotic compactness of solutions by Balls idea of energy equations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
