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.
Produkt-Info
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Illustrationen
3
2 farbige Abbildungen, 3 s/w Abbildungen
VIII, 166 p. 5 illus., 2 illus. in color.
Maße
Höhe: 240 mm
Breite: 168 mm
Dicke: 10 mm
Gewicht
ISBN-13
978-3-031-12030-5 (9783031120305)
DOI
10.1007/978-3-031-12031-2
Schweitzer Klassifikation
Professor Lee
got his PhD at Yonsei University in Seoul after receiving his bachelor's degree from the University of Washington in Seattle. He iscurrently an Assistant Professor of Mathematics at Chonnam National University in Gwangju, Republic of Korea. His research interests include PDE and Dynamical Systems.
Professor Morales Rojas
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.
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.
