04629nam 2200709 a 450 991045652480332120200520144314.01-283-16682-897866131668213-11-025529-410.1515/9783110255294(CKB)2550000000042910(EBL)797998(OCoLC)749781836(SSID)ssj0000530409(PQKBManifestationID)11339104(PQKBTitleCode)TC0000530409(PQKBWorkID)10567594(PQKB)10842858(MiAaPQ)EBC797998(WaSeSS)Ind00009646(DE-B1597)123627(OCoLC)840437417(DE-B1597)9783110255294(Au-PeEL)EBL797998(CaPaEBR)ebr10486432(CaONFJC)MIL316682(EXLCZ)99255000000004291020110224d2011 uy 0engur|n|---|||||txtccrBlow-up in nonlinear Sobolev type equations[electronic resource] /Alexander B. Alʹshin, Maxim O. Korpusov, Alexey G. SveshnikovBerlin ;New York De Gruyterc20111 online resource (660 p.)De Gruyter series in nonlinear analysis and applications,0941-8183X ;15Description based upon print version of record.3-11-025527-8 Includes bibliographical references and index. Frontmatter -- Preface -- Contents -- Chapter 0 Introduction -- Chapter 1 Nonlinear model equations of Sobolev type -- Chapter 2 Blow-up of solutions of nonlinear equations of Sobolev type -- Chapter 3 Blow-up of solutions of strongly nonlinear Sobolev-type wave equations and equations with linear dissipation -- Chapter 4 Blow-up of solutions of strongly nonlinear, dissipative wave Sobolev-type equations with sources -- Chapter 5 Special problems for nonlinear equations of Sobolev type -- Chapter 6 Numerical methods of solution of initial-boundary-value problems for Sobolev-type equations -- Appendix A Some facts of functional analysis -- Appendix B To Chapter 6 -- Bibliography -- IndexThe 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. De Gruyter series in nonlinear analysis and applications ;15.Initial value problemsNumerical solutionsNonlinear difference equationsMathematical physicsElectronic books.Initial value problemsNumerical solutions.Nonlinear difference equations.Mathematical physics.515/.782Alʹshin A. B1038727Korpusov M. O1034924Sveshnikov A. G(Alekseĭ Georgievich),1924-53188MiAaPQMiAaPQMiAaPQBOOK9910456524803321Blow-up in nonlinear Sobolev type equations2460504UNINA01175nam0 22003011i 450 UON0051868420231205105534.98338-04-41713-220231018d2001 |0itac50 bagerDE|||| |||||Erläuterungen zu Frühlings ErwachenFrank Wedekindvon Thomas MobiusHollfeldBange Verlag2001114 p.18 cm001UON001745752001 Königs Erläuterungen und Materialen210 HollfeldC. Bange Verlag.406NARRATIVA TEDESCAUONC084005FIHollfeldUONL003572830Letteratura tedesca21WEDEKINDFrankUONV123054158645MOBIUSThomasUONV292485Bange VerlagUONV268005650ITSOL20240220RICASIBA - SISTEMA BIBLIOTECARIO DI ATENEOUONSIUON00518684SIBA - SISTEMA BIBLIOTECARIO DI ATENEOSI F. Goethe 830 WED 4410 SI 46343 5 4410 Erläuterungen zu Frühlings Erwachen3904596UNIOR