UID:
almahu_9949481320002882
Format:
1 online resource (648 p.)
ISBN:
9783110255294
,
9783110647099
Series Statement:
De Gruyter Series in Nonlinear Analysis and Applications , 15
Content:
The 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.
Note:
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 --
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Chapter 5 Special problems for nonlinear equations of Sobolev type --
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Chapter 6 Numerical methods of solution of initial-boundary-value problems for Sobolev-type equations --
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Appendix A Some facts of functional analysis --
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Appendix B To Chapter 6 --
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Bibliography --
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Index
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Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DG Studies in Nonlinear Analysis and Applications, De Gruyter, 9783110647099
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011, De Gruyter, 9783110261189
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011, De Gruyter, 9783110261233
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011, De Gruyter, 9783110261202
Additional Edition:
ISBN 9783110255270
Language:
English
Subjects:
Mathematics
DOI:
10.1515/9783110255294
URL:
https://doi.org/10.1515/9783110255294
URL:
https://www.degruyter.com/isbn/9783110255294
URL:
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