LEADER 04458nam 22005895 450 001 9910819097903321 005 20240516010750.0 010 $a1-4612-0873-4 024 7 $a10.1007/978-1-4612-0873-0 035 $a(CKB)3400000000089300 035 $a(SSID)ssj0001298441 035 $a(PQKBManifestationID)11686519 035 $a(PQKBTitleCode)TC0001298441 035 $a(PQKBWorkID)11241627 035 $a(PQKB)10351096 035 $a(DE-He213)978-1-4612-0873-0 035 $a(MiAaPQ)EBC3073820 035 $a(PPN)238032868 035 $a(EXLCZ)993400000000089300 100 $a20121227d1994 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aShock Waves and Reaction?Diffusion Equations /$fby Joel Smoller 205 $a2nd ed. 1994. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1994. 215 $a1 online resource (XXIII, 634 p.) 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v258 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-94259-9 311 $a1-4612-6929-6 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aFor this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con­ structing travelling waves for systems of nonlinear equations. The final sec­ tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica­ ble to many interesting reaction-diffusion systems. 410 0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v258 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aAnalysis. 676 $a515 700 $aSmoller$b Joel$4aut$4http://id.loc.gov/vocabulary/relators/aut$057297 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819097903321 996 $aShock Waves and Reaction?Diffusion Equations$93971674 997 $aUNINA