LEADER 03751nam 22005775 450 001 9910338246403321 005 20240226215842.0 010 $a3-030-18222-3 024 7 $a10.1007/978-3-030-18222-9 035 $a(CKB)4100000008424480 035 $a(DE-He213)978-3-030-18222-9 035 $a(MiAaPQ)EBC5926764 035 $a(PPN)24860225X 035 $a(EXLCZ)994100000008424480 100 $a20190613d2019 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSuperlinear Parabolic Problems $eBlow-up, Global Existence and Steady States /$fby Prof. Dr. Pavol Quittner, Prof. Dr. Philippe Souplet 205 $a2nd ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019. 215 $a1 online resource (XXII, 719 p. 15 illus.) 225 1 $aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 311 $a3-030-18220-7 327 $aModel Elliptic Problems -- Model Parabolic Problems -- Systems -- Equations with Gradient Terms -- Nonlocal Problems. 330 $aThis book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition. 410 0$aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 606 $aDifferential equations 606 $aPotential theory (Mathematics) 606 $aFunctional analysis 606 $aDifferential Equations 606 $aPotential Theory 606 $aFunctional Analysis 615 0$aDifferential equations. 615 0$aPotential theory (Mathematics). 615 0$aFunctional analysis. 615 14$aDifferential Equations. 615 24$aPotential Theory. 615 24$aFunctional Analysis. 676 $a515.353 700 $aQuittner$b P$g(Pavol)$4aut$4http://id.loc.gov/vocabulary/relators/aut$0723729 702 $aSouplet$b Philippe$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910338246403321 996 $aSuperlinear Parabolic Problems$94113404 997 $aUNINA