INVARIANT FOLIATIONS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH NON-DENSE DOMAIN

Authors：Zeng, Caibin^*; Shen, Jun

Source：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150(5): 2023-2036.

DOI：10.1090/proc/15686

• INTEGRATED SEMIGROUPS
• MANIFOLD THEOREM
• EXPONENTS

In this paper we study the existence of Lipschitz invariant stable and unstable foliations for a class of stochastic partial differential equations with non-dense domain. We would like to emphasize that the linear part neither generates a C-0 semigroup nor satisfies the Hille-Yosida condition. Using the theory of integrated semigroup and Lyapunov-Perron method, we establish the main result to trace the long-term behavior of such an equation and apply it to a stochastic parabolic equation.

• Institution
  四川大学