The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations write by Salah-Eldin Mohammed. This book was released on 2008. The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations available in PDF, EPUB and Kindle. The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations and stochastic partial differential equations near stationary solutions.
Effective Dynamics of Stochastic Partial Differential Equations
Effective Dynamics of Stochastic Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Effective Dynamics of Stochastic Partial Differential Equations write by Jinqiao Duan. This book was released on 2014-03-06. Effective Dynamics of Stochastic Partial Differential Equations available in PDF, EPUB and Kindle. Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. - New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty - Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations - Solutions or hints to all Exercises
Amplitude Equations for Stochastic Partial Differential Equations
Amplitude Equations for Stochastic Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Amplitude Equations for Stochastic Partial Differential Equations write by Dirk Blomker. This book was released on 2007. Amplitude Equations for Stochastic Partial Differential Equations available in PDF, EPUB and Kindle. Rigorous error estimates for amplitude equations are well known for deterministic PDEs, and there is a large body of literature over the past two decades. However, there seems to be a lack of literature for stochastic equations, although the theory is being successfully used in the applied community, such as for convective instabilities, without reliable error estimates at hand. This book is the first step in closing this gap. The author provides details about the reduction of dynamics to more simpler equations via amplitude or modulation equations, which relies on the natural separation of time-scales present near a change of stability. For students, the book provides a lucid introduction to the subject highlighting the new tools necessary for stochastic equations, while serving as an excellent guide to recent research.
Probability and Partial Differential Equations in Modern Applied Mathematics
Probability and Partial Differential Equations in Modern Applied Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Probability and Partial Differential Equations in Modern Applied Mathematics write by Edward C. Waymire. This book was released on 2010-06-14. Probability and Partial Differential Equations in Modern Applied Mathematics available in PDF, EPUB and Kindle. "Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.
Approximation of Stochastic Invariant Manifolds
Approximation of Stochastic Invariant Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximation of Stochastic Invariant Manifolds write by Mickaël D. Chekroun. This book was released on 2014-12-20. Approximation of Stochastic Invariant Manifolds available in PDF, EPUB and Kindle. This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
