LEADER 04745nam 2200769 a 450 001 9910823037403321 005 20240514052927.0 010 $a1-283-16682-8 010 $a9786613166821 010 $a3-11-025529-4 024 7 $a10.1515/9783110255294 035 $a(CKB)2550000000042910 035 $a(EBL)797998 035 $a(OCoLC)749781836 035 $a(SSID)ssj0000530409 035 $a(PQKBManifestationID)11339104 035 $a(PQKBTitleCode)TC0000530409 035 $a(PQKBWorkID)10567594 035 $a(PQKB)10842858 035 $a(MiAaPQ)EBC797998 035 $a(WaSeSS)Ind00009646 035 $a(DE-B1597)123627 035 $a(OCoLC)840437417 035 $a(DE-B1597)9783110255294 035 $a(Au-PeEL)EBL797998 035 $a(CaPaEBR)ebr10486432 035 $a(CaONFJC)MIL316682 035 $a(EXLCZ)992550000000042910 100 $a20110224d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBlow-up in nonlinear Sobolev type equations /$fAlexander B. Al?shin, Maxim O. Korpusov, Alexey G. Sveshnikov 205 $a1st ed. 210 $aBerlin ;$aNew York $cDe Gruyter$dc2011 215 $a1 online resource (660 p.) 225 1 $aDe Gruyter series in nonlinear analysis and applications,$x0941-8183X ;$v15 300 $aDescription based upon print version of record. 311 $a3-11-025527-8 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tPreface -- $tContents -- $tChapter 0 Introduction -- $tChapter 1 Nonlinear model equations of Sobolev type -- $tChapter 2 Blow-up of solutions of nonlinear equations of Sobolev type -- $tChapter 3 Blow-up of solutions of strongly nonlinear Sobolev-type wave equations and equations with linear dissipation -- $tChapter 4 Blow-up of solutions of strongly nonlinear, dissipative wave Sobolev-type equations with sources -- $tChapter 5 Special problems for nonlinear equations of Sobolev type -- $tChapter 6 Numerical methods of solution of initial-boundary-value problems for Sobolev-type equations -- $tAppendix A Some facts of functional analysis -- $tAppendix B To Chapter 6 -- $tBibliography -- $tIndex 330 $aThe monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the blow-up time. The abstract results apply to a large variety of problems. Thus, the well-known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with sources and many other physical problems are considered as examples. Moreover, the method proposed for studying blow-up phenomena for nonlinear Sobolev-type equations is applied to equations which play an important role in physics. For instance, several examples describe different electrical breakdown mechanisms in crystal semiconductors, as well as the breakdown in the presence of sources of free charges in a self-consistent electric field. The monograph contains a vast list of references (440 items) and gives an overall view of the contemporary state-of-the-art of the mathematical modeling of various important problems arising in physics. Since the list of references contains many papers which have been published previously only in Russian research journals, it may also serve as a guide to the Russian literature. 410 0$aDe Gruyter series in nonlinear analysis and applications ;$v15. 606 $aInitial value problems$xNumerical solutions 606 $aNonlinear difference equations 606 $aMathematical physics 610 $aBlow up. 610 $aCauchy problem. 610 $aNonlinear equations. 610 $aSobolev. 615 0$aInitial value problems$xNumerical solutions. 615 0$aNonlinear difference equations. 615 0$aMathematical physics. 676 $a515/.782 686 $aSK 540$qSEPA$2rvk 700 $aAl?shin$b A. B$01660103 701 $aKorpusov$b M. O$01034924 701 $aSveshnikov$b A. G$g(Aleksei? Georgievich),$f1924-$053188 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910823037403321 996 $aBlow-up in nonlinear Sobolev type equations$94015114 997 $aUNINA