Interdisciplinary Mathematical Sciences: Stochastic PDEs and Modelling of Multiscale Complex System (ePub)

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.

• Preface
• A Biographical Note and Tribute to Anthony Roberts on His 60th Birthday
• Geometric Methods for Stochastic Dynamical Systems (Jinqiao Duan and Hui Wang)
• Stochastic 3D Navier–Stokes Equations with Nonlinear Damping: Martingale Solution, Strong Solution and Small Time LDP (Hongjun Gao and Hui Liu)
• Model Reduction in Stochastic Environments (E Forgoston, L Billings and I B Schwartz)
• An Averaging Principle for Multi-valued Stochastic Differential Equations Driven by G-Brownian Motion (Yong Xu, Min Han and Bin Pei)
• Optimal Control for the Nonlocal Backward Heat Equation (Xiaoli Wang, Jinchun He, Haoyuan Xu and Meihua Yang)
• Hölder Estimates for Solutions of Stochastic Nonlocal Diffusion Equations (Guangying Lv, Hongjun Gao, Jinlong Wei, Jiang-Lun Wu)
• Multiscale Modelling Couples Patches of Two-Layer Thin Fluid Flow (Meng Cao and A J Roberts)
• The Cauchy Problem for a Generalized Ostrovsky Equation with Positive Dispersion(Wei Yan)
• Well-Posedness for Stochastic Two Component Dullin-Gottwald-Holm System with Lévy Noise (Yong Chen and Jingyun Luo)
• On Smooth Approximation of Lévy Processes in Skorokhod Space (Lingyu Feng, Xianming Liu)
• Error Estimation on Projective Integration of Expensive Multiscale Stochastic Simulation(Xiaopeng Chen and A J Roberts)
• Approximation for Stochastic Wave Equations with Singular Perturbation (Yan Lv and Wei Wang)