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＜E-Book＞
Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs / by Jihoon Lee, Carlos Morales
(Frontiers in Mathematics. ISSN:16608054)

Edition	1st ed. 2022.
Publisher	(Cham : Springer International Publishing : Imprint: Birkhäuser)
Year	2022
Size	VIII, 166 p. 5 illus., 2 illus. in color : online resource
Authors	*Lee, Jihoon author Morales, Carlos author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Differential equations LCSH:Geometry, Differential FREE:Dynamical Systems FREE:Differential Equations FREE:Differential Geometry
Notes	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. HTTP:URL=https://doi.org/10.1007/978-3-031-12031-2

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