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Gromov-hausdorff stability of dynamical systems and applications to PDEs

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Gromov-hausdorff stability of dynamical systems and applications to PDEsby Jihoon Lee, Carlos Morales.
作者:	Lee, Jihoon.
其他作者:	Morales, Carlos.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	viii, 166 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Geometry, Differential.
電子資源:	https://doi.org/10.1007/978-3-031-12031-2
ISBN:	9783031120312$q(electronic bk.)

Gromov-hausdorff stability of dynamical systems and applications to PDEs
Lee, Jihoon.

Gromov-hausdorff stability of dynamical systems and applications to PDEs[electronic resource] /by Jihoon Lee, Carlos Morales. - Cham :Springer International Publishing :2022. - viii, 166 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8054. - Frontiers in mathematics..

Part I: Abstract Theory -- Gromov-Hausdorff distances -- Stability -- Continuity of Shift Operator -- Shadowing from Gromov-Hausdorff Viewpoint -- Part II: Applications to PDEs -- GH-Stability of Reaction Diffusion Equation -- Stability of Inertial Manifolds -- Stability of Chafee-Infante Equations.

This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance. In the first part, the authors introduce the notion of Gromov-Hausdorff distance between compact metric spaces, along with the corresponding distance for continuous maps, flows, and group actions on these spaces. They also focus on the stability of certain dynamical objects like shifts, global attractors, and inertial manifolds. Applications to dissipative PDEs, such as the reaction-diffusion and Chafee-Infante equations, are explored in the second part. This text will be of interest to graduates students and researchers working in the areas of topological dynamics and PDEs.

ISBN: 9783031120312$q(electronic bk.)

Standard No.: 10.1007/978-3-031-12031-2doiSubjects--Topical Terms:

182610
Geometry, Differential.

LC Class. No.: QA641 / .L44 2022

Dewey Class. No.: 516.36

Gromov-hausdorff stability of dynamical systems and applications to PDEs
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520 $a This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance. In the first part, the authors introduce the notion of Gromov-Hausdorff distance between compact metric spaces, along with the corresponding distance for continuous maps, flows, and group actions on these spaces. They also focus on the stability of certain dynamical objects like shifts, global attractors, and inertial manifolds. Applications to dissipative PDEs, such as the reaction-diffusion and Chafee-Infante equations, are explored in the second part. This text will be of interest to graduates students and researchers working in the areas of topological dynamics and PDEs.
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