Details
Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs
Frontiers in Mathematics
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21,39 € |
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| Verlag: | Birkhäuser |
| Format: | |
| Veröffentl.: | 30.10.2022 |
| ISBN/EAN: | 9783031120312 |
| Sprache: | englisch |
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Beschreibungen
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.
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.
<b></b><b>Professor Lee</b> got his PhD at Yonsei University in Seoul after receiving his bachelor's degree from the University of Washington in Seattle. He is<div>currently an Assistant Professor of Mathematics at Chonnam National University in Gwangju, Republic of Korea. His research interests include PDE and Dynamical Systems.</div><div><br></div><b>Professor Morales Rojas</b> got his PhD at IMPA, Rio de Janeiro, Brazil. He is currently Associated Professor at the Federal University of Rio de Janeiro, Brazil. His research interests include Dynamical Systems and its applications.<div><br></div><div><div><br></div></div><div><br></div>
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.
Presents novel insights into the perturbation theory of dynamical systems based on Gromov-Hausdorff distance Develops a perturbation theory of PDEs where both the equation and the domain are perturbed Explores several applications to PDEs, including the reaction diffusion and Chafee-Infante equations
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