03614nam 2200577 450 99649516750331620230421132438.03-031-12031-0(MiAaPQ)EBC7127696(Au-PeEL)EBL7127696(CKB)25219360800041(PPN)265856167(EXLCZ)992521936080004120230316d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGromov-Hausdorff stability of dynamical systems and applications to PDEs /Jihoon Lee and Carlos MoralesCham, Switzerland :Birkhäuser,[2022]©20221 online resource (169 pages)Frontiers in mathematicsPrint version: Lee, Jihoon Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs Cham : Springer International Publishing AG,c2023 9783031120305 Includes bibliographical references.Intro -- Preface -- Contents -- Part I Abstract Theory -- 1 Gromov-Hausdorff Distances -- 1.1 Introduction -- 1.2 Preliminary Facts -- 1.3 Gromov-Hausdorff Distance for Metric Spaces -- 1.4 Precompactness, Completeness, and a Variational Principle -- 1.5 A Variational Principle for the Gromov-Hausdorff Distance -- 1.6 Distances Characterizing Homeomorphic Spaces -- 1.7 C0-Gromov-Hausdorff Distance for Dynamical Systems -- 1.8 Gromov-Hausdorff Space of Continuous Maps -- Exercises -- 2 Stability -- 2.1 Introduction -- 2.2 Definitions and Statement of Main Results -- 2.3 Proof of Theorem 2.1 -- 2.4 Isometric Stability: Proof of Theorem 2.4 -- 2.5 Proof of Theorem 2.5 -- 2.6 Gromov-Hausdorff Stability for Group Actions -- 2.7 Gromov-Hausdorff Stability of Global Attractors -- Exercises -- 3 Continuity of the Shift Operator -- 3.1 Introduction -- 3.2 Preliminary Facts -- 3.3 Proof of Theorem 3.1 -- 3.4 Application to Stability Theory -- Exercises -- 4 Shadowing from the Gromov-Hausdorff Viewpoint -- 4.1 Introduction -- 4.2 Definitions, Statement of Main Results, and Proofs -- Exercises -- Part II Applications to PDEs -- Introduction -- 5 GH-Stability of Reaction-Diffusion Equations -- 5.1 Introduction -- 5.2 Proof of Theorem 5.1 -- 5.3 Proof of Theorem 5.2 -- 6 Stability of Inertial Manifolds -- 6.1 Introduction -- 6.2 Proof of Theorem 6.2 -- 6.3 Proof of Theorem 6.3 -- 7 Stability of Chafee-Infante Equations -- 7.1 Introduction -- 7.2 L-Morse-Smale and Equivalence of Global Attractors -- 7.3 Continuity of Global Attractors -- 7.4 Geometric Stability -- References.Frontiers in mathematics.Differentiable dynamical systemsDifferential equations, PartialGeometry, DifferentialSistemes dinàmics diferenciablesthubEquacions en derivades parcialsthubGeometria diferencialthubLlibres electrònicsthubDifferentiable dynamical systems.Differential equations, Partial.Geometry, Differential.Sistemes dinàmics diferenciablesEquacions en derivades parcialsGeometria diferencial515.352Lee Jihoon1263810Rojas Carlos Arnoldo MoralesMiAaPQMiAaPQMiAaPQBOOK996495167503316Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs2962669UNISA