随机偏微分方程的有效动力学（英文版）
出版时间:
2016-01
版次:
1
ISBN:
9787560357645
定价:
88.00
装帧:
平装
开本:
16开
纸张:
胶版纸
页数:
270页
字数:
355千字
正文语种:
英语
-
《随机偏微分方程的有效动力学（英文版）》主要介绍了随机偏微分方程与时间测度、空间测度之间的关系。内容包括平均值、同质化、从随机偏微方程里面提取有效的动力学等。《随机偏微分方程的有效动力学（英文版）》内容深刻全面，涵盖面广，对学习研究偏微分的人具有很大地帮助。《随机偏微分方程的有效动力学（英文版）》可作为相关专业本科生及研究生参考书。 Preface
1 Introduction
1．1 Motivation
1．2 Examples of Stochastic Partial Differential Equations
1．3 Outlines for This Book
2 Deterministic Partial Differential Equations
2．1 Fourier Series in Hilbert Space
2．2 Solving Linear Partial Differential Equations
2．3 Integral Equalities
2．4 Differential and Integral Inequalities
2．5 Sobolev Inequalities
2．6 Some Nonlinear Partial Differential Equations
2．7 Problems
3 Stochastic Calculus in Hilbert Space
3．1 Brownian Motion and White Noise in Euclidean Space
3．2 Deterministic Calculus in Hilbert Space
3．3 Random Variables in Hilbert Space
3．4 Gaussian Random Variables in Hilbert Space
3．5 Brownian Motion and White Noise in Hilbert Space
3．6 Stochastic Calculus in Hilbert Space
3．7 It6's Formula in Hilbert Space
3．8 Problems
4 Stochastic Partial Differential Equations
4．1 Basic Setup
4．2 Strong and Weak Solutions
4．3 Mild Solutions
4．4 Martingale Solutions
4．5 Conversion Between It6 and Stratonovich SPDEs
4．6 Linear Stochastic Partial Differential Equations
4．7 Effects of Noise on Solution Paths
4．8 Large Deviations for SPDEs
4．9 Infinite Dimensional Stochastic Dynamics
4．10 Random Dynamical Systems Defined by SPDEs
4．11 Problems
5 Stochastic Averaging Principles
5．1 Classical Results on Averaging
5．2 An Averaging Principle for Slow-Fast SPDEs
5．3 Proof of the Averaging Principle Theorem 5．20
5．4 A Normal Deviation Principle for Slow-Fast SPDEs
5．5 Proof of the Normal Deviation Principle Theorem 5．34
5．6 Macroscopic Reduction for Stochastic Systems
5．7 Large Deviation Principles for the Averaging Approximation
5．8 PDEs with Random Coefficients
5．9 Further Remarks
5．10 Looking Forward
5．11 Problems
6 Slow Manifold Reduction
6．1 Background
6．2 Random Center-Unstable Manifolds for Stochastic Systems
6．3 Random Center-Unstable Manifold Reduction
6．4 Local Random Invariant Manifold for SPDEs
6．5 Random Slow Manifold Reduction for Slow-Fast SPDEs
6．6 A Different Reduction Method for SPDEs： Amplitude Equation
6．7 Looking Forward
6．8 Problems
7 Stochastic Homogenization
7．1 Deterministic Homogenization
7．2 Homogenized Macroscopic Dynamics for Stochastic Linear Microscopic Systems
7．3 Homogenized Macroscopic Dynamics for Stochastic Nonlinear Microscopic Systems
7．4 Looking Forward
7．5 Problems
Hints and Solutions
Notations
References
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内容简介:
《随机偏微分方程的有效动力学（英文版）》主要介绍了随机偏微分方程与时间测度、空间测度之间的关系。内容包括平均值、同质化、从随机偏微方程里面提取有效的动力学等。《随机偏微分方程的有效动力学（英文版）》内容深刻全面，涵盖面广，对学习研究偏微分的人具有很大地帮助。《随机偏微分方程的有效动力学（英文版）》可作为相关专业本科生及研究生参考书。
-
目录:
Preface
1 Introduction
1．1 Motivation
1．2 Examples of Stochastic Partial Differential Equations
1．3 Outlines for This Book
2 Deterministic Partial Differential Equations
2．1 Fourier Series in Hilbert Space
2．2 Solving Linear Partial Differential Equations
2．3 Integral Equalities
2．4 Differential and Integral Inequalities
2．5 Sobolev Inequalities
2．6 Some Nonlinear Partial Differential Equations
2．7 Problems
3 Stochastic Calculus in Hilbert Space
3．1 Brownian Motion and White Noise in Euclidean Space
3．2 Deterministic Calculus in Hilbert Space
3．3 Random Variables in Hilbert Space
3．4 Gaussian Random Variables in Hilbert Space
3．5 Brownian Motion and White Noise in Hilbert Space
3．6 Stochastic Calculus in Hilbert Space
3．7 It6's Formula in Hilbert Space
3．8 Problems
4 Stochastic Partial Differential Equations
4．1 Basic Setup
4．2 Strong and Weak Solutions
4．3 Mild Solutions
4．4 Martingale Solutions
4．5 Conversion Between It6 and Stratonovich SPDEs
4．6 Linear Stochastic Partial Differential Equations
4．7 Effects of Noise on Solution Paths
4．8 Large Deviations for SPDEs
4．9 Infinite Dimensional Stochastic Dynamics
4．10 Random Dynamical Systems Defined by SPDEs
4．11 Problems
5 Stochastic Averaging Principles
5．1 Classical Results on Averaging
5．2 An Averaging Principle for Slow-Fast SPDEs
5．3 Proof of the Averaging Principle Theorem 5．20
5．4 A Normal Deviation Principle for Slow-Fast SPDEs
5．5 Proof of the Normal Deviation Principle Theorem 5．34
5．6 Macroscopic Reduction for Stochastic Systems
5．7 Large Deviation Principles for the Averaging Approximation
5．8 PDEs with Random Coefficients
5．9 Further Remarks
5．10 Looking Forward
5．11 Problems
6 Slow Manifold Reduction
6．1 Background
6．2 Random Center-Unstable Manifolds for Stochastic Systems
6．3 Random Center-Unstable Manifold Reduction
6．4 Local Random Invariant Manifold for SPDEs
6．5 Random Slow Manifold Reduction for Slow-Fast SPDEs
6．6 A Different Reduction Method for SPDEs： Amplitude Equation
6．7 Looking Forward
6．8 Problems
7 Stochastic Homogenization
7．1 Deterministic Homogenization
7．2 Homogenized Macroscopic Dynamics for Stochastic Linear Microscopic Systems
7．3 Homogenized Macroscopic Dynamics for Stochastic Nonlinear Microscopic Systems
7．4 Looking Forward
7．5 Problems
Hints and Solutions
Notations
References
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