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221107 ||| eng |
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|a 9783031120312
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|a Lee, Jihoon
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| 245 |
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|a Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs
|h Elektronische Ressource
|c by Jihoon Lee, Carlos Morales
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| 250 |
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|a 1st ed. 2022
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| 260 |
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|a Cham
|b Birkhäuser
|c 2022, 2022
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| 300 |
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|a VIII, 166 p. 5 illus., 2 illus. in color
|b online resource
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|a 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
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| 653 |
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|a Geometry, Differential
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| 653 |
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|a Dynamical Systems
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| 653 |
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|a Differential Geometry
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| 653 |
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|a Differential Equations
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| 653 |
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|a Differential equations
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| 653 |
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|a Dynamical systems
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| 700 |
1 |
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|a Morales, Carlos
|e [author]
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Frontiers in Mathematics
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| 028 |
5 |
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|a 10.1007/978-3-031-12031-2
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-031-12031-2?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515.39
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| 520 |
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|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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