Blow-up in Nonlinear Sobolev Type Equations (De Gruyter Series in Nonlinear Analysis and Applications)

Alexander B. Al'shin

ISBN 10: 3110255278 / ISBN 13: 9783110255270

Published by De Gruyter, 2011

About this Item

in plastic wrap.

Seller Inventory # mon0003352153

Bibliographic Details

• Title: Blow-up in Nonlinear Sobolev Type Equations (De Gruyter Series in Nonlinear Analysis and Applications)
• Publisher: De Gruyter
• Publication Date: 2011
• Language: English
• ISBN 10: 3110255278
• ISBN 13: 9783110255270
• Binding: Hardcover
• Condition: Fine

About this title

Synopsis

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.

About the Author

Alexander B. Al'shin, Maxim O. Korpusov, Alexey G. Sveshnikov, Lomonosov Moscow State University, Russia.