EDP Sciences 1776165823 20260414 fre

laboutique.edpsciences.fr-R001710 03 01 01 R001710 00 ED E107 00 01 01 Attractors for Nonlinear Autonomous Dynamical Systems 01 eng 08 226 03 22 2376377 17 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 11 00 20220621 02 01 002093 03 9782759827039 15 9782759827039 03 01 D1 EDP Sciences 45 03 laboutique.edpsciences.fr-002093 03 01 01 002093 03 9782759827039 15 9782759827039 10 EA E107 10 00 01 R001710 ED E107 1 10 01 02 Current Natural Sciences 01 01 Attractors for Nonlinear Autonomous Dynamical Systems 1 A01 01 A2052 Yuming Qin Qin, Yuming Yuming Qin Dr. Yuming QIN is full professor, head of Mathematics Department and director of Institute of Nonlinear Sciences of Donghua University. His research interests are global (local) wellposedness of solutions and infinite-dimensional dynamical systems for nonlinear evolutionary equations including fluid equations such as Navier–Stokes equations, MHD, etc, and thermo(visco)elasticequations.<o:p></o:p> 2 A01 01 A2053 Keqin Su Su, Keqin Keqin Su Dr. Keqin SU is associate professor in College of Information and ManagementScience, Henan Agricultural University since 2020.<o:p></o:p> 1 01 eng 08 224 03 01 24 Izibook:Subject Mathématiques 24 Izibook:SubjectAndCategoryAndTags |Mathématiques| 20 mathematics;infinite-dimensional dynamical systems;partial differential equations;fluid mechanics;autonomous nonlinear evolutionary equations;Navier–Stokes equations;Navier–Stokes–Voight systems;nonlinear thermoviscoelastic system 10 2011 BISACMAT040000 01 510 06 05 03 00 This book introduces complete and systematic theories of infinite-dimensional dynamical systems and their applications in partial differential equations, especially in the models of fluid mechanics. It is based on the first author’s lecture “Infinite dimensional dynamical systems on nonlinear autonomous systems” given to graduate students in Donghua University since 2004. This book presents recent results that have been carried out by the authors on autonomous nonlinear evolutionar yequations arising from physics, fluid mechanics and material science such as the Navier–Stokes equations, Navier–Stokes–Voight systems, the nonlinear thermoviscoelastic system, etc. This book introduces complete and systematic theories of infinite-dimensional dynamical systems and their applications in partial differential equations, especially in the models of fluid mechanics. It is based on the first author’s lecture “Infinite dimensional dynamical systems on nonlinear autonomous systems” given tograduate students in Donghua University since 2004. This book presents recent results that have been carried out by the authors on autonomous nonlinear evolutionary equations arising from physics, fluid mechanics and material science such as the Navier–Stokes equations, Navier–Stokes–Voight systems, the nonlinearthermoviscoelastic system, etc. 02 00 <span lang="EN-US" style="font-size:9.0pt;line-height:107%;font-family:MilibusLt-Regular;mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-family:MilibusLt-Regular;mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA">This book introducescomplete and systematic theories of infinite-dimensional dynamical systems andtheir applications in partial differential equations, especially in the models offluid mechanics. This book presents recent results that have been carried outby the authors on autonomous nonlinear evolutionary equations arising fromphysics, fluid mechanics and material science such as the Navier–Stokesequations, Navier–Stokes–Voight systems, the nonlinear thermoviscoelastic system,etc 04 00 ContentsPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IXCHAPTER 1Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Some Useful Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Basic Theory of Infinite-Dimensional Dynamical Systems for Autonomous Nonlinear Evolutionary Equations . . . . . . . . . . . . . . . 101.2.1 Uniformly Compact Semigroups . . . . . . . . . . . . . . . . . . . . . . . . 101.2.2 Weakly Compact Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . 161.2.3 X-Limit Compact Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . 171.2.4 Asymptotically Compact Semigroups . . . . . . . . . . . . . . . . . . . . 221.2.5 Asymptotically Smooth Semigroups . . . . . . . . . . . . . . . . . . . . . 271.2.6 Norm-to-Weak Continuous Semigroups. . . . . . . . . . . . . . . . . . . 281.2.7 Closed Operator Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . 301.3 Basic Theory of Finite-Dimensional Attractors . . . . . . . . . . . . . . . . . . 321.3.1 The Fractal Dimension of Global Attractors . . . . . . . . . . . . . . . 321.3.2 The Estimate on Fractal Dimension of Global Attractors . . . . . 33CHAPTER 2Global Attractors for the Navier–Stokes–Voight Equations with Delay . . . . . 372.1 Global Wellposedness of Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2 Existence of Global Attractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.2.1 Dissipation: Existence of Absorbing Sets . . . . . . . . . . . . . . . . . 432.2.2 Asymptotical Compactness and Existence of Attractor . . . . . . . 442.3 Bibliographic Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46CHAPTER 3Global Attractor and Its Upper Estimate on Fractal Dimensionfor the 2D Navier–Stokes–Voight Equations . . . . . . . . . . . . . . . . . . . . . . . . . 473.1 Global Existence of Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Existence of Global Attractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.2.1 Existence of Absorbing Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.2.2 Some Compactness and the Existence of Global Attractors . . . 563.3 Upper Estimate on the Fractal Dimension of Global Attractors . . . . . . 583.4 Bibliographic Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64CHAPTER 4Maximal Attractor for the Equations of One-Dimensional CompressiblePolytropic Viscous Ideal Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.1 Our Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.2 Nonlinear Semigroup on Hð2Þ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.3 Existence of an Absorbing Set in Hð1Þ b . . . . . . . . . . . . . . . . . . . . . . . . . 734.4 Existence of an Absorbing Set in Hð2Þ b . . . . . . . . . . . . . . . . . . . . . . . . . 834.5 Proof of Theorem 4.2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.6 Bibliographic Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88CHAPTER 5Universal Attractors for a Nonlinear System of CompressibleOne-Dimensional Heat-Conducting Viscous Real Gas . . . . . . . . . . . . . . . . . . 915.1 Main Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.2 Nonlinear C0-Semigroup on Hiþ ði ¼ 1; 2Þ. . . . . . . . . . . . . . . . . . . . . . . 955.3 Existence of an Absorbing Set in H1d . . . . . . . . . . . . . . . . . . . . . . . . . . 975.4 Existence of an Absorbing Set in H2d . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.5 Proof of Theorem 5.1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.6 Bibliographic Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111CHAPTER 6Global Attractors for the Compressible Navier–Stokes Equations in Bounded Annular Domains . . . . . . . . . . . . . . . . . . . . . . . 1156.1 Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1156.2 Nonlinear Semigroup on Hð2Þ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.3 Existence of an Absorbing Set in Hð1Þ d . . . . . . . . . . . . . . . . . . . . . . . . . 1206.4 Existence of an Absorbing Set in Hð2Þ d . . . . . . . . . . . . . . . . . . . . . . . . . 1296.5 Existence of an Absorbing Set in Hð4Þ d . . . . . . . . . . . . . . . . . . . . . . . . . 1356.6 Bibliographic Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146CHAPTER 7Global Attractor for a Nonlinear Thermoviscoelastic System in Shape Memory Alloys . . . . . . . . . . . . . .. . . . . . . . . . . 1497.1 Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1497.2 An Absorbing Set Bd in Hd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1527.3 Compactness of the Orbit in Hd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1657.4 Bibliographic Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173CHAPTER 8Global Attractors for Nonlinear Reaction–Diffusion Equations and the 2D Navier–Stokes Equations . . . . . . . .. . . . . . . . . . . . . . . . . 1758.1 Global Attractor for Strong Solutions of Reaction–Diffusion Equations . . 1758.1.1 Existence of Solutions and Uniqueness . . . . . . . . . . . . . . . . . . . 1768.1.2 Global Attractor for the Semigroup in LpðXÞ . . . . . . . . . . . . . . 1768.1.3 Global Attractor of System in LpðXÞ and H10 ðXÞ . . . . . . . . . . . . 1778.2 Global Attractors for the 2D Navier–Stokes Equations in H10 ðXÞ . . . . . 183CHAPTER 9Global Attractors for an Incompressible Fluid Equation and a Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1879.1 An Incompressible Fluid Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1879.2 AWave Equation with Nonlinear Damping . . . . . . . . . . . . . . . . . . . . . 1939.2.1 Wellposedness of Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1949.2.2 Dissipativity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1969.2.3 Asymptotic Compactness and Existence of Global Attractor . . 200References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 21 00 06 01 https://laboutique.edpsciences.fr/produit/1270/9782759827039/attractors-for-nonlinear-autonomous-dynamical-systems 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/982/664/original/9782759827022-Attractors_for_Nonlinear_Autonomous_Systems_couv-sofedis.jpg 17 14 20240913T184216+0200 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 11 00 20220621 01 00 20220621 19 00 20220621 2026 06 3052868830012 01 WORLD 13 03 9782759827022 15 9782759827022 WORLD 08 EDP Sciences & Science Press 04 01 00 20220621 03 01 D1 EDP Sciences 20 04 05 01 02 1 00 54.99 01 5.50 2.87 EUR 04 06 01 02 1 00 191.99 01 5.50 2.87 EUR 01 04 06 01 02 1 00 211.99 01 5.50 11.05 USD 01