Volume 32, Issue 2
Approximation of Smooth Stable Invariant Manifolds for Stochastic Partial Differential Equations

Zhongkai Guo, Xingjie Yan & Xin-Guang Yang

J. Part. Diff. Eq., 32 (2019), pp. 112-128.

Published online: 2019-07

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  • Abstract

Invariant manifolds are complicate random sets useful for describing and understanding the qualitative behavior of nonlinear dynamical systems. The purpose of the present paper is try to approximate smooth stable invariant manifolds for a type of stochastic partial differential equations with multiplicative white noise near the fixed point. Two examples are given to illustrate our results.

  • Keywords

Stochastic partial differential equation smooth stable invariant manifold geometric shape analytical approximation.

  • AMS Subject Headings

35B40, 35B41, 35Q30, 76D03, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhongkaiguo@hust.edu.cn (Zhongkai Guo)

yanxj04@163.com (Xingjie Yan)

yangxinguang@hotmail.com (Xin-Guang Yang)

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  • RIS
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@Article{JPDE-32-112, author = {Guo , Zhongkai and Yan , Xingjie and Yang , Xin-Guang }, title = {Approximation of Smooth Stable Invariant Manifolds for Stochastic Partial Differential Equations}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {32}, number = {2}, pages = {112--128}, abstract = {

Invariant manifolds are complicate random sets useful for describing and understanding the qualitative behavior of nonlinear dynamical systems. The purpose of the present paper is try to approximate smooth stable invariant manifolds for a type of stochastic partial differential equations with multiplicative white noise near the fixed point. Two examples are given to illustrate our results.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n2.2}, url = {http://global-sci.org/intro/article_detail/jpde/13237.html} }
TY - JOUR T1 - Approximation of Smooth Stable Invariant Manifolds for Stochastic Partial Differential Equations AU - Guo , Zhongkai AU - Yan , Xingjie AU - Yang , Xin-Guang JO - Journal of Partial Differential Equations VL - 2 SP - 112 EP - 128 PY - 2019 DA - 2019/07 SN - 32 DO - http://dor.org/10.4208/jpde.v32.n2.2 UR - https://global-sci.org/intro/jpde/13237.html KW - Stochastic partial differential equation KW - smooth stable invariant manifold KW - geometric shape KW - analytical approximation. AB -

Invariant manifolds are complicate random sets useful for describing and understanding the qualitative behavior of nonlinear dynamical systems. The purpose of the present paper is try to approximate smooth stable invariant manifolds for a type of stochastic partial differential equations with multiplicative white noise near the fixed point. Two examples are given to illustrate our results.

Zhongkai Guo , Xingjie Yan & Xin-Guang Yang . (2019). Approximation of Smooth Stable Invariant Manifolds for Stochastic Partial Differential Equations. Journal of Partial Differential Equations. 32 (2). 112-128. doi:10.4208/jpde.v32.n2.2
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