Evolutionary equations. (2007)

• Record Type: Book
• Further Information: Note: Edited by C.M. Dafermos, E. Feireisl.
• Other Names: Dafermos, C. M (Constantine M.); Feireisl, Eduard
• Contents: Front cover; Titel page; Copyright page; Preface; List of Contributors; Contents; Contents of Volume I; Contents of Volume II; Chapter 1 Gradient Flows of Probability Measures; Introduction; 1. Notation and measure-theoretic results; 2. Metric and differentiable structure of the Wasserstein space; 3. Convex functionals in P2(Rd); 4. Subdifferential calculus in P2(Rd); 5. Gradient flows of lambda-geodesically convex functionals in P2(Rd); 6. Applications to evolution PDEs; References; Chapter 2 The Mathematics of Chemotaxis; 1. Introduction: What is chemotaxis? 2. How do chemotactic units work?3. Some mathematical problems arising from the study of Dictyostelium discoideum; Acknowledgements; References; Chapter 3 Examples of Singular Limits in Hydrodynamics; 1. Introduction; 2. The inviscid limit; 3. Compressible-incompressible limit; 4. Study of rotating fluids at high frequency; 5. Hydrodynamic limit of the Boltzmann equation; 6. Some homogenization problems; 7. Conclusion; Acknowledgement; References; Chapter 4 Notes on Hyperbolic Systems of Conservation Laws and Transport Equations; 1. Introduction; 2. Preliminaries. 3. DiPerna-Lions theory for nearly incompressible flows4. Commutator estimates and Ambrosio's renormalization theorem; 5. Existence, uniqueness, and stability for the Keyfitz and Kranzer system; 6. Blow-up of the BV norm for the Keyfitz and Kranzer system; 7. Partial regularity and trace properties of solutions to transport equations; 8. Bressan's compactness conjecture and the renormalization conjecture for nearly incompressible BV vector fields; 9. Tangential sets of BV vector fields; Acknowledgements; References. Chapter 5 Collisionless Kinetic Equations from Astrophysics -- The Vlasov-Poisson SystemIntroduction; Notation and preliminaries; 1. Classical solutions to the initial value problem; 2. Stability; References; Chapter 6 Stochastic Representations for Nonlinear Parabolic PDEs; 1. Introduction; 2. Linear case: Feynman-Kac representation; 3. Representation via controlled processes; 4. Backward representations; 5. Monte Carlo methods; Acknowledgement; References; Chapter 7 Controllability and Observability of Partial Differential Equations: Some Results and Open Problems; 1. Introduction. 2. Preliminaries on finite-dimensional systems3. Controllability of the linear wave equation; 4. The heat equation; 5. Sharp observability estimates for the linear heat equation; 6. Parabolic equations with low regularity coefficients; 7. Fluid-structure interaction models; 8. Some open problems; Acknowledgements; References; Author Index; Subject Index.
• Publisher Details: Amsterdam Boston : Elsevier/North Holland
• Publication Date: 2007
• Extent: 1 online resource (xiii, 638 pages), illustrations
• Subjects: 515/.35; Differential equations -- Handbooks, manuals, etc; Mathematical analysis; Differential equations -- Handbooks, manuals, etc; Mathematical analysis; MATHEMATICS -- Differential Equations -- General; Differential equations; Mathematical analysis; Electronic books; Handbooks and manuals
• Languages: English
• ISBNs: 9780080465654
• Related ISBNs: 008046565X; 0444528482
• Notes: Note: Includes bibliographical references and indexes.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.