Mohammed S.-E.A. The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations / S.-E.A.Mohammed, T.Zhang, H.Zhao. - Providence: American Mathematical Society, 2008. - vi, 105 p.: ill. - (Memoirs of the American Mathematical Society; Vol.196, N 917). - Bibliogr.: p.103-105. - ISBN 978-0-8218-4250-8; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Introduction .................................................... 1 Part 1. The stochastic semiflow §1.1 Basic concepts ............................................. 6 §1.2 Flows and cocycles of semilinear see's ..................... 7 (a) Linear see's ........................................... 8 (b) Semilinear see's ...................................... 27 §1.3 Semilinear spde's: Lipschitz nonlinearity ................. 35 §1.4 Semilinear spde's: Non-Lipschitz nonlinearity ............. 44 (a) Stochastic reaction diffusion equations ............... 44 (b) Burgers equation with additive noise .................. 58 Part 2. Existence of stable and unstable manifolds §2.1 Hyperbolicity of a stationary trajectory .................. 69 §2.2 The nonlinear ergodic theorem ............................. 73 §2.3 Proof of the local stable manifold theorem ................ 77 §2.4 The local stable manifold theorem for see's and spde's .... 95 (a) See's: Additive noise ................................. 95 (b) Semilinear see's: Linear noise ........................ 98 (c) Semilinear parabolic spde's: Lipschitz nonlinearity ......................................... 100 (d) Stochastic reaction diffusion equations: Dissipative nonlinearity ............................. 100 (e) Stochastic Burgers equation: Additive noise .......... 101 Acknowledgments ............................................... 102 Bibliography .................................................. 103