Shock Waves and Reaction—Diffusion Equations / / by Joel Smoller

• Autore: Smoller Joel
• Pubblicazione: New York, NY : , : Springer New York : , : Imprint : Springer, , 1994
• Edizione: 2nd ed. 1994.
• Descrizione fisica: 1 online resource (XXIII, 634 p.)
• Disciplina: 515
• Soggetto topico: Mathematical analysis; Analysis (Mathematics); Analysis
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 1 Ill-Posed Problems -- 2 Characteristics and Initial-Value Problems -- 3 The One-Dimensional Wave Equation -- 4 Uniqueness and Energy Integrals -- 5 Holmgren’s Uniqueness Theorem -- 6 An Initial-Value Problem for a Hyperbolic Equation -- 7 Distribution Theory -- 8 Second-Order Linear Elliptic Equations -- 9 Second-Order Linear Parabolic Equations -- 10 Comparison Theorems and Monotonicity Methods -- 11 Linearization -- 12 Topological Methods -- 13 Bifurcation Theory -- 14 Systems of Reaction-Diffusion Equations -- 15 Discontinuous Solutions of Conservation Laws -- 16 The Single Conservation Law -- 17 The Riemann Problem for Systems of Conservation Laws -- 18 Applications to Gas Dynamics -- 19 The Glimm Difference Scheme -- 20 Riemann Invariants, Entropy, and Uniqueness -- 21 Quasi-Linear Parabolic Systems -- 22 The Conley Index -- 23 Index Pairs and the Continuation Theorem -- 24 Travelling Waves -- 25 Recent Results -- Author Index.
• Sommario/riassunto: For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con­ structing travelling waves for systems of nonlinear equations. The final sec­ tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica­ ble to many interesting reaction-diffusion systems.
• Titolo autorizzato: Shock Waves and Reaction—Diffusion Equations
• ISBN: 1-4612-0873-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910819097903321
• Lo trovi qui: Univ. Federico II
• Serie: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, . 0072-7830 ; ; 258