Evolution equations :: long time behavior and control /
The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as...
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, England :
Cambridge University Press,
2018.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
439. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations. |
| Beschreibung: | 1 online resource (194 pages) |
| ISBN: | 1108331033 9781108331036 |
Internformat
MARC
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 439 | |
| 520 | |a The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations. | ||
| 505 | 0 | |a Cover -- Series Page -- Title page -- Imprints Page -- Contents -- Preface -- List of Contributors Present at the Summer School -- 1 Controllability of Parabolic Systems: The Moment Method -- 1.1 Introduction -- 1.2 Parabolic Systems and Controllability Concepts -- 1.3 Controllability Results for the Scalar Case: The Carleman Inequality -- 1.4 First Application to a Parabolic System -- 1.5 The Moment Method -- 1.5.1 Presentation: Example 1 -- 1.5.2 Generalization of the Moment Problem -- 1.5.3 Going Back to the Heat Equation | |
| 505 | 8 | |a 1.5.4 Example 2: A Minimal Time of Control for a 2 x 2 Parabolic System due to the Coupling Function 1.5.5 Example 3: A Minimal Time of Control Due to the Condensation of the Eigenvalues of the System -- 1.6 The Index of Condensation -- 1.6.1 Definition -- 1.6.2 Optimal Condensation Grouping -- 1.6.3 Interpolating Function -- 1.6.4 An Interpolating Formula of Jensen -- 1.6.5 Going Back to the Boundary Control Problem -- References -- 2 Stabilization of Semilinear PDEs, and Uniform Decay under Discretization -- 2.1 Introduction and General Results | |
| 505 | 8 | |a 2.1.1 General Setting2.1.2 In Finite Dimension -- 2.1.3 In Infinite Dimension -- 2.1.4 Existing Results for Discretizations -- 2.1.5 Conclusion -- 2.2 Parabolic PDEs -- 2.3 Hyperbolic PDEs -- 2.3.1 The Continuous Setting -- 2.3.2 Space Semidiscretizations -- 2.3.3 Time Semidiscretizations -- 2.3.4 Full Discretizations -- 2.3.5 Conclusion and Open Problems -- References -- 3 A Null-Controllability Result for the Linear System of Thermoelastic Plates with a Single Control -- 3.1 Introduction and Main Results -- 3.2 Solutions in Series Form | |
| 505 | 8 | |a 3.3 Control of the Cascade System3.4 Appendix -- References -- 4 Doubly Connected V-States for the Generalized Surface Quasi-geostrophic Equations -- 4.1 Introduction and Main Result -- 4.2 Boundary Equations -- 4.3 Basic Tools -- 4.3.1 Functional Spaces -- 4.3.2 Crandallâ#x80;#x93;Rabinowitz's Theorem -- 4.3.3 Special Functions -- 4.4 Regularity of the Nonlinear Functional -- 4.5 Spectral Study -- 4.5.1 Linearized Operator -- 4.5.2 Monotonicity of the Eigenvalues -- 4.6 Bifurcation at Simple Eigenvalues -- References | |
| 505 | 8 | |a 5 About Least-Squares Type Approach to Address Direct and Controllability Problems5.1 Introduction -- 5.2 A Least-Squares Reformulation -- 5.3 Convergence of Some Minimizing Sequences for -- 5.4 Direct Problem for the Steady Navierâ#x80;#x93;Stokes System -- References -- 6 A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay -- 6.1 Introduction -- 6.2 Well-Posedness -- 6.3 Stability Results -- 6.4 Examples -- 6.4.1 The Wave Equation -- 6.4.2 The Elasticity System -- 6.4.3 The Mindlinâ#x80;#x93;Timoshenko Model -- 6.4.4 The Petrovsky System | |
| 650 | 0 | |a Evolution equations. |0 http://id.loc.gov/authorities/subjects/sh85046035 | |
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| contents | Cover -- Series Page -- Title page -- Imprints Page -- Contents -- Preface -- List of Contributors Present at the Summer School -- 1 Controllability of Parabolic Systems: The Moment Method -- 1.1 Introduction -- 1.2 Parabolic Systems and Controllability Concepts -- 1.3 Controllability Results for the Scalar Case: The Carleman Inequality -- 1.4 First Application to a Parabolic System -- 1.5 The Moment Method -- 1.5.1 Presentation: Example 1 -- 1.5.2 Generalization of the Moment Problem -- 1.5.3 Going Back to the Heat Equation 1.5.4 Example 2: A Minimal Time of Control for a 2 x 2 Parabolic System due to the Coupling Function 1.5.5 Example 3: A Minimal Time of Control Due to the Condensation of the Eigenvalues of the System -- 1.6 The Index of Condensation -- 1.6.1 Definition -- 1.6.2 Optimal Condensation Grouping -- 1.6.3 Interpolating Function -- 1.6.4 An Interpolating Formula of Jensen -- 1.6.5 Going Back to the Boundary Control Problem -- References -- 2 Stabilization of Semilinear PDEs, and Uniform Decay under Discretization -- 2.1 Introduction and General Results 2.1.1 General Setting2.1.2 In Finite Dimension -- 2.1.3 In Infinite Dimension -- 2.1.4 Existing Results for Discretizations -- 2.1.5 Conclusion -- 2.2 Parabolic PDEs -- 2.3 Hyperbolic PDEs -- 2.3.1 The Continuous Setting -- 2.3.2 Space Semidiscretizations -- 2.3.3 Time Semidiscretizations -- 2.3.4 Full Discretizations -- 2.3.5 Conclusion and Open Problems -- References -- 3 A Null-Controllability Result for the Linear System of Thermoelastic Plates with a Single Control -- 3.1 Introduction and Main Results -- 3.2 Solutions in Series Form 3.3 Control of the Cascade System3.4 Appendix -- References -- 4 Doubly Connected V-States for the Generalized Surface Quasi-geostrophic Equations -- 4.1 Introduction and Main Result -- 4.2 Boundary Equations -- 4.3 Basic Tools -- 4.3.1 Functional Spaces -- 4.3.2 Crandallâ#x80;#x93;Rabinowitz's Theorem -- 4.3.3 Special Functions -- 4.4 Regularity of the Nonlinear Functional -- 4.5 Spectral Study -- 4.5.1 Linearized Operator -- 4.5.2 Monotonicity of the Eigenvalues -- 4.6 Bifurcation at Simple Eigenvalues -- References 5 About Least-Squares Type Approach to Address Direct and Controllability Problems5.1 Introduction -- 5.2 A Least-Squares Reformulation -- 5.3 Convergence of Some Minimizing Sequences for -- 5.4 Direct Problem for the Steady Navierâ#x80;#x93;Stokes System -- References -- 6 A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay -- 6.1 Introduction -- 6.2 Well-Posedness -- 6.3 Stability Results -- 6.4 Examples -- 6.4.1 The Wave Equation -- 6.4.2 The Elasticity System -- 6.4.3 The Mindlinâ#x80;#x93;Timoshenko Model -- 6.4.4 The Petrovsky System |
| ctrlnum | (OCoLC)1013733130 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-on1013733130 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:28:07Z |
| institution | BVB |
| isbn | 1108331033 9781108331036 |
| language | English |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Evolution equations : long time behavior and control / edited by Kaïs Ammari, Stéphane Gerbi. Cambridge, England : Cambridge University Press, 2018. ß2018 1 online resource (194 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 439 The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations. Cover -- Series Page -- Title page -- Imprints Page -- Contents -- Preface -- List of Contributors Present at the Summer School -- 1 Controllability of Parabolic Systems: The Moment Method -- 1.1 Introduction -- 1.2 Parabolic Systems and Controllability Concepts -- 1.3 Controllability Results for the Scalar Case: The Carleman Inequality -- 1.4 First Application to a Parabolic System -- 1.5 The Moment Method -- 1.5.1 Presentation: Example 1 -- 1.5.2 Generalization of the Moment Problem -- 1.5.3 Going Back to the Heat Equation 1.5.4 Example 2: A Minimal Time of Control for a 2 x 2 Parabolic System due to the Coupling Function 1.5.5 Example 3: A Minimal Time of Control Due to the Condensation of the Eigenvalues of the System -- 1.6 The Index of Condensation -- 1.6.1 Definition -- 1.6.2 Optimal Condensation Grouping -- 1.6.3 Interpolating Function -- 1.6.4 An Interpolating Formula of Jensen -- 1.6.5 Going Back to the Boundary Control Problem -- References -- 2 Stabilization of Semilinear PDEs, and Uniform Decay under Discretization -- 2.1 Introduction and General Results 2.1.1 General Setting2.1.2 In Finite Dimension -- 2.1.3 In Infinite Dimension -- 2.1.4 Existing Results for Discretizations -- 2.1.5 Conclusion -- 2.2 Parabolic PDEs -- 2.3 Hyperbolic PDEs -- 2.3.1 The Continuous Setting -- 2.3.2 Space Semidiscretizations -- 2.3.3 Time Semidiscretizations -- 2.3.4 Full Discretizations -- 2.3.5 Conclusion and Open Problems -- References -- 3 A Null-Controllability Result for the Linear System of Thermoelastic Plates with a Single Control -- 3.1 Introduction and Main Results -- 3.2 Solutions in Series Form 3.3 Control of the Cascade System3.4 Appendix -- References -- 4 Doubly Connected V-States for the Generalized Surface Quasi-geostrophic Equations -- 4.1 Introduction and Main Result -- 4.2 Boundary Equations -- 4.3 Basic Tools -- 4.3.1 Functional Spaces -- 4.3.2 Crandallâ#x80;#x93;Rabinowitz's Theorem -- 4.3.3 Special Functions -- 4.4 Regularity of the Nonlinear Functional -- 4.5 Spectral Study -- 4.5.1 Linearized Operator -- 4.5.2 Monotonicity of the Eigenvalues -- 4.6 Bifurcation at Simple Eigenvalues -- References 5 About Least-Squares Type Approach to Address Direct and Controllability Problems5.1 Introduction -- 5.2 A Least-Squares Reformulation -- 5.3 Convergence of Some Minimizing Sequences for -- 5.4 Direct Problem for the Steady Navierâ#x80;#x93;Stokes System -- References -- 6 A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay -- 6.1 Introduction -- 6.2 Well-Posedness -- 6.3 Stability Results -- 6.4 Examples -- 6.4.1 The Wave Equation -- 6.4.2 The Elasticity System -- 6.4.3 The Mindlinâ#x80;#x93;Timoshenko Model -- 6.4.4 The Petrovsky System Evolution equations. http://id.loc.gov/authorities/subjects/sh85046035 Équations d'évolution. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ecuaciones de evolución embucm Evolution equations fast Ammari, Kaïs, editor. http://id.loc.gov/authorities/names/no2014157367 Gerbi, Stéphane, editor. http://id.loc.gov/authorities/names/nb2017021840 Print version: Evolution equations. Cambridge, England : Cambridge University Press, 2018 1108412300 9781108412308 (OCoLC)989038627 London Mathematical Society lecture note series ; 439. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1602645 Volltext |
| spellingShingle | Evolution equations : long time behavior and control / London Mathematical Society lecture note series ; Cover -- Series Page -- Title page -- Imprints Page -- Contents -- Preface -- List of Contributors Present at the Summer School -- 1 Controllability of Parabolic Systems: The Moment Method -- 1.1 Introduction -- 1.2 Parabolic Systems and Controllability Concepts -- 1.3 Controllability Results for the Scalar Case: The Carleman Inequality -- 1.4 First Application to a Parabolic System -- 1.5 The Moment Method -- 1.5.1 Presentation: Example 1 -- 1.5.2 Generalization of the Moment Problem -- 1.5.3 Going Back to the Heat Equation 1.5.4 Example 2: A Minimal Time of Control for a 2 x 2 Parabolic System due to the Coupling Function 1.5.5 Example 3: A Minimal Time of Control Due to the Condensation of the Eigenvalues of the System -- 1.6 The Index of Condensation -- 1.6.1 Definition -- 1.6.2 Optimal Condensation Grouping -- 1.6.3 Interpolating Function -- 1.6.4 An Interpolating Formula of Jensen -- 1.6.5 Going Back to the Boundary Control Problem -- References -- 2 Stabilization of Semilinear PDEs, and Uniform Decay under Discretization -- 2.1 Introduction and General Results 2.1.1 General Setting2.1.2 In Finite Dimension -- 2.1.3 In Infinite Dimension -- 2.1.4 Existing Results for Discretizations -- 2.1.5 Conclusion -- 2.2 Parabolic PDEs -- 2.3 Hyperbolic PDEs -- 2.3.1 The Continuous Setting -- 2.3.2 Space Semidiscretizations -- 2.3.3 Time Semidiscretizations -- 2.3.4 Full Discretizations -- 2.3.5 Conclusion and Open Problems -- References -- 3 A Null-Controllability Result for the Linear System of Thermoelastic Plates with a Single Control -- 3.1 Introduction and Main Results -- 3.2 Solutions in Series Form 3.3 Control of the Cascade System3.4 Appendix -- References -- 4 Doubly Connected V-States for the Generalized Surface Quasi-geostrophic Equations -- 4.1 Introduction and Main Result -- 4.2 Boundary Equations -- 4.3 Basic Tools -- 4.3.1 Functional Spaces -- 4.3.2 Crandallâ#x80;#x93;Rabinowitz's Theorem -- 4.3.3 Special Functions -- 4.4 Regularity of the Nonlinear Functional -- 4.5 Spectral Study -- 4.5.1 Linearized Operator -- 4.5.2 Monotonicity of the Eigenvalues -- 4.6 Bifurcation at Simple Eigenvalues -- References 5 About Least-Squares Type Approach to Address Direct and Controllability Problems5.1 Introduction -- 5.2 A Least-Squares Reformulation -- 5.3 Convergence of Some Minimizing Sequences for -- 5.4 Direct Problem for the Steady Navierâ#x80;#x93;Stokes System -- References -- 6 A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay -- 6.1 Introduction -- 6.2 Well-Posedness -- 6.3 Stability Results -- 6.4 Examples -- 6.4.1 The Wave Equation -- 6.4.2 The Elasticity System -- 6.4.3 The Mindlinâ#x80;#x93;Timoshenko Model -- 6.4.4 The Petrovsky System Evolution equations. http://id.loc.gov/authorities/subjects/sh85046035 Équations d'évolution. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ecuaciones de evolución embucm Evolution equations fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85046035 |
| title | Evolution equations : long time behavior and control / |
| title_auth | Evolution equations : long time behavior and control / |
| title_exact_search | Evolution equations : long time behavior and control / |
| title_full | Evolution equations : long time behavior and control / edited by Kaïs Ammari, Stéphane Gerbi. |
| title_fullStr | Evolution equations : long time behavior and control / edited by Kaïs Ammari, Stéphane Gerbi. |
| title_full_unstemmed | Evolution equations : long time behavior and control / edited by Kaïs Ammari, Stéphane Gerbi. |
| title_short | Evolution equations : |
| title_sort | evolution equations long time behavior and control |
| title_sub | long time behavior and control / |
| topic | Evolution equations. http://id.loc.gov/authorities/subjects/sh85046035 Équations d'évolution. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Ecuaciones de evolución embucm Evolution equations fast |
| topic_facet | Evolution equations. Équations d'évolution. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Ecuaciones de evolución Evolution equations |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1602645 |
| work_keys_str_mv | AT ammarikais evolutionequationslongtimebehaviorandcontrol AT gerbistephane evolutionequationslongtimebehaviorandcontrol |