Invariant Sets and Global Attractor of a Class of Partial Differential Equations

2001 ◽  
pp. 419-429
Author(s):  
Daoyi Xu ◽  
Qingyi Guo
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Attractor ◽  
Invariant Sets ◽  
Partial Differential

Exponential global attractors for semigroups in metric spaces with applications to differential equations

2011 ◽  
Vol 31 (6) ◽  
pp. 1641-1667 ◽  
Author(s):  
ALEXANDRE N. CARVALHO ◽  
JAN W. CHOLEWA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Attractor ◽  
Metric Space ◽  
Metric Spaces ◽  
Global Attractors ◽  
Invariant Sets ◽  
Bounded Subset ◽  
Partial Differential ◽  
Unstable Manifolds

AbstractIn this article semigroups in a general metric space V, which have pointwise exponentially attracting local unstable manifolds of compact invariant sets, are considered. We show that under a suitable set of assumptions these semigroups possess strong exponential dissipative properties. In particular, there exists a compact global attractor which exponentially attracts each bounded subset of V. Applications of abstract results to ordinary and partial differential equations are given.

On smooth approximation for random attractor of stochastic partial differential equations with multiplicative noise

2018 ◽  
Vol 18 (05) ◽  
pp. 1850040 ◽  
Author(s):  
Hongbo Fu ◽  
Xianming Liu ◽  
Jicheng Liu ◽  
Xiangjun Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Random Attractor ◽  
Invariant Sets ◽  
Stochastic Pdes ◽  
Polygonal Approximation ◽  
Smooth Approximation ◽  
Partial Differential ◽  
Random Partial Differential Equations

Wong–Zakai type approximation for stochastic partial differential equations (abbreviate as PDEs) is well studied. Besides the polygonal approximation, a type of smooth noise approximation is considered. After showing the existence of random attractor for a class of random partial differential equations defined on the entire space [Formula: see text], when random color noises tend to white noise, the solutions and invariant sets between original stochastic PDEs and random PDEs are compared. Some continuity results of random attractor in random dynamical systems are indicated.

Sign in / Sign up

Export Citation Format

Share Document