Blow-Up in Nonlinear Sobolev Type Equations 9783110255270

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Автор: Al`shin Alexander B., Korpusov Maxim O., Sveshnikov Alexey G.
Название: Blow-Up in Nonlinear Sobolev Type Equations
ISBN: 9783110255270
Издательство: Walter de Gruyter
Издательство: de Gruyter
Классификация:

Дифференциальное исчисление и дифференциальные уравнения

ISBN-10: 3110255278
Обложка/Формат: Hardcover
Страницы: 660
Вес: 1.24 кг.
Дата издания: 17.05.2011
Серия: De gruyter series in nonlinear analysis & applications
Язык: English
Размер: 24.41 x 16.99 x 3.66 cm
Читательская аудитория: Professional & vocational
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Поставляется из: США
Описание:

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.

Blow-Up in Nonlinear Sobolev Type Equations, Al`shin Alexander B., Korpusov Maxim O., Sveshnikov Alexey G.