By Alexander B. Al'shin,Maxim O. Korpusov,Alexey G. Sveshnikov
The monograph is dedicated to the examine of initial-boundary-value difficulties for multi-dimensional Sobolev-type equations over bounded domain names. The authors ponder either particular initial-boundary-value difficulties and summary Cauchy difficulties for first-order (in the time variable) differential equations with nonlinear operator coefficients with admire to spatial variables. the most objective of the monograph is to acquire enough stipulations for worldwide (in time) solvability, to acquire adequate stipulations for blow-up of suggestions at finite time, and to derive higher and decrease estimates for the blow-up time.
The summary effects practice to a wide number of difficulties. hence, the well known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with resources and lots of different actual difficulties are regarded as examples. additionally, the tactic proposed for learning blow-up phenomena for nonlinear Sobolev-type equations is utilized to equations which play a huge function in physics. for example, a number of examples describe assorted electric breakdown mechanisms in crystal semiconductors, in addition to the breakdown within the presence of assets of loose fees in a self-consistent electrical field.
The monograph features a enormous record of references (440 goods) and provides an total view of the modern cutting-edge of the mathematical modeling of assorted vital difficulties coming up in physics. because the record of references comprises many papers which were released formerly merely in Russian study journals, it may well additionally function a consultant to the Russian literature.
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Additional resources for Blow-up in Nonlinear Sobolev Type Equations (De Gruyter Series in Nonlinear Analysis and Applications)
Blow-up in Nonlinear Sobolev Type Equations (De Gruyter Series in Nonlinear Analysis and Applications) by Alexander B. Al'shin,Maxim O. Korpusov,Alexey G. Sveshnikov