scholarly journals Mean-square invariant manifolds for ill-posed stochastic evolution equations driven by nonlinear noise

2022 ◽  
Vol 313 ◽  
pp. 382-419
Author(s):  
Zonghao Li ◽  
Caibin Zeng ◽  
Jianhua Huang
Keyword(s):  
Invariant Manifolds ◽  
Evolution Equations ◽  
Mean Square ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Ill Posed ◽  
Nonlinear Noise

Random invariant manifolds for ill-posed stochastic evolution equations

2019 ◽  
Vol 20 (02) ◽  
pp. 2050013
Author(s):  
Alexandra Neamţu
Keyword(s):  
Invariant Manifolds ◽  
Evolution Equations ◽  
Linear Part ◽  
Time Behavior ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Stable And Unstable Manifolds ◽  
Long Time ◽  
Ill Posed ◽  
Unstable Manifolds

We establish the existence of random stable and unstable manifolds for ill-posed stochastic partial differential equations (SPDEs). Namely, we assume that the linear part does not generate a [Formula: see text]-semigroup. Using the theory of integrated semigroups, we are able to analyze the long-time behavior of random dynamical systems generated by such SPDEs.

scholarly journals Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density

1981 ◽  
Vol 84 ◽  
pp. 195-208 ◽  
Author(s):  
B. L. Rozovskii ◽  
A. Shimizu
Keyword(s):  
Evolution Equations ◽  
Transition Density ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Smoothness Of Solutions

In this paper, we shall discuss the smoothness of solutions of stochastic evolution equations, which has been investigated in N. V. Krylov and B. L. Rozovskii [2] [3], to establish the existence of a filtering transition density.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

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