Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs
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Beschreibung
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.
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
Autor*in
Jihoon Lee
Themen in »Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs«
Gromov-Hausdorff distance Stability of dynamical systems Gromov-Hausdorff stability Shadowing Property Global Attractor Inertial Manifold Shift operator