Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs

Jihoon Lee, Carlos Morales (Autoren)

Buch | Softcover

VIII, 166 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-12030-5 (ISBN)

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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.

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.

Erscheinungsdatum	01.11.2022
Reihe/Serie	Frontiers in Mathematics
Zusatzinfo	VIII, 166 p. 5 illus., 2 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	168 x 240 mm
Gewicht	308 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Technik ► Maschinenbau
Schlagworte	global attractor • Gromov-Hausdorff distance • Gromov-Hausdorff stability • Inertial Manifold • Shadowing Property • Shift operator • stability of dynamical systems
ISBN-10	3-031-12030-2 / 3031120302
ISBN-13	978-3-031-12030-5 / 9783031120305
Zustand	Neuware