LEADER 03082nam 22006255 450 001 9910624380003321 005 20251113175200.0 010 $a3-031-12031-0 024 7 $a10.1007/978-3-031-12031-2 035 $a(MiAaPQ)EBC7127696 035 $a(Au-PeEL)EBL7127696 035 $a(CKB)25219360800041 035 $a(PPN)265856167 035 $a(OCoLC)1351219412 035 $a(DE-He213)978-3-031-12031-2 035 $a(EXLCZ)9925219360800041 100 $a20221030d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs /$fby Jihoon Lee, Carlos Morales 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2022. 215 $a1 online resource (169 pages) 225 1 $aFrontiers in Mathematics,$x1660-8054 311 08$aPrint version: Lee, Jihoon Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs Cham : Springer International Publishing AG,c2023 9783031120305 320 $aIncludes bibliographical references. 327 $aPart 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. 330 $aThis monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance. In the first part, the authors introduce the notion of Gromov-Hausdorff distance between compact metric spaces, along with the corresponding distance for continuous maps, flows, and group actions on these spaces. They also focus on the stability of certain dynamical objects like shifts, global attractors, and inertial manifolds. Applications to dissipative PDEs, such as the reaction-diffusion and Chafee-Infante equations, are explored in the second part. This text will be of interest to graduates students and researchers working in the areas of topological dynamics and PDEs. . 410 0$aFrontiers in Mathematics,$x1660-8054 606 $aDynamics 606 $aDifferential equations 606 $aGeometry, Differential 606 $aDynamical Systems 606 $aDifferential Equations 606 $aDifferential Geometry 615 0$aDynamics. 615 0$aDifferential equations. 615 0$aGeometry, Differential. 615 14$aDynamical Systems. 615 24$aDifferential Equations. 615 24$aDifferential Geometry. 676 $a515.352 676 $a516.36 700 $aLee$b Jihoon$01263810 702 $aRojas$b Carlos Arnoldo Morales 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910624380003321 996 $aGromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs$92962669 997 $aUNINA