A remark on reaction-diffusion equations in unbounded domains
نویسندگان
چکیده
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 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 کاملExistence and Uniqueness of Invariant Measures for Stochastic Reaction–Diffusion Equations in Unbounded Domains
In this paper, we investigate the long-time behavior of stochastic reaction– diffusion equations of the type du = (Au + f (u))dt + σ(u)dW (t), where A is an elliptic operator, f and σ are nonlinear maps and W is an infinite-dimensional nuclear Wiener process.The emphasis is onunboundeddomains.Under the assumption that the nonlinear function f possesses certain dissipative properties, this equat...
متن کاملReaction-diffusion equations with nonlinear boundary conditions in narrow domains
Second initial boundary problem in narrow domains of width ǫ ≪ 1 for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution of such a problem converges as ǫ ↓ 0 to the solution of a standard reaction-diffusion equation in a domain of reduced dimension. This reduction allows to obtain some r...
متن کاملKernel Sections of Multi-valued Processes with Application to the Nonlinear Reaction-diffusion Equations in Unbounded Domains
First, we introduce the concept of pullback ω-limit compactness for multivalued processes, as an extension of the similar concept in the autonomous and nonautonomous framework. Next, we present the necessary and sufficient conditions (pullback dissipativeness and pullback ω-limit compactness) for the existence of a nonempty local bounded kernel (kernel sections are all compact, invariant and pu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2002
ISSN: 1078-0947
DOI: 10.3934/dcds.2003.9.281