LEADER 03231nam 22006135 450 001 9910254290903321 005 20200706152835.0 010 $a3-662-55725-8 024 7 $a10.1007/978-3-662-55725-9 035 $a(CKB)4340000000223611 035 $a(DE-He213)978-3-662-55725-9 035 $a(MiAaPQ)EBC5162658 035 $a(PPN)221247661 035 $a(EXLCZ)994340000000223611 100 $a20171125d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNonlinear Wave Equations /$fby Tatsien Li, Yi Zhou 205 $a1st ed. 2017. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2017. 215 $a1 online resource (XVI, 391 p. 2 illus.) 225 1 $aSeries in Contemporary Mathematics,$x2364-009X ;$v2 311 $a3-662-55723-1 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Linear Wave functions -- Sobolev inequality with Decay -- Estimates for solutions for linear wave equation -- Estimates for composition Function. 330 $aThis book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle. 410 0$aSeries in Contemporary Mathematics,$x2364-009X ;$v2 606 $aDifferential equations, Partial 606 $aDifference equations 606 $aFunctional equations 606 $aCalculus of variations 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 615 0$aDifferential equations, Partial. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aCalculus of variations. 615 14$aPartial Differential Equations. 615 24$aDifference and Functional Equations. 615 24$aCalculus of Variations and Optimal Control; Optimization. 676 $a515.625 700 $aLi$b Tatsien$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755910 702 $aZhou$b Yi$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254290903321 996 $aNonlinear Wave Equations$92028762 997 $aUNINA