The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations. Memoirs of the American Mathematical Society; 917.

Mohammed, Salah-eldin A.; Zhang, Tusheng; Zhao. Huaizhong

ISBN 10: 0821842501 / ISBN 13: 9780821842508

Editore: Providence, American Mathematical Society, 2008

Riguardo questo articolo

Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-00433 9780821842508 Sprache: Englisch Gewicht in Gramm: 150. Codice articolo 2482944

Dati bibliografici

Titolo: The stable manifold theorem for semilinear ...

Casa editrice: Providence, American Mathematical Society

Data di pubblicazione: 2008

Legatura: Softcover

Descrizione articolo

Riassunto:

The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis is in two parts.In Part 1, the authors prove general existence and compactness theorems for $C^k$-cocycles of semilinear see's and spde's. The results cover a large class of semilinear see's as well as certain semilinear spde's with Lipschitz and non-Lipschitz terms such as stochastic reaction diffusion equations and the stochastic Burgers equation with additive infinite-dimensional noise. In Part 2, stationary solutions are viewed as cocycle-invariant random points in the infinite-dimensional state space. The pathwise local structure of solutions of semilinear see's and spde's near stationary solutions is described in terms of the almost sure longtime behavior of trajectories of the equations in relation to the stationary solution.