By Alexander B. Al'shin,Maxim O. Korpusov,Alexey G. Sveshnikov

The monograph is dedicated to the learn 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 recognize to spatial variables. the most objective of the monograph is to acquire adequate stipulations for international (in time) solvability, to procure adequate stipulations for blow-up of ideas at finite time, and to derive top and reduce estimates for the blow-up time.

The summary effects practice to a wide number of difficulties. therefore, the well known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with resources and plenty of different actual difficulties are regarded as examples. furthermore, the strategy proposed for learning blow-up phenomena for nonlinear Sobolev-type equations is utilized to equations which play a major 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 large record of references (440 goods) and provides an total view of the modern state of the art of the mathematical modeling of assorted very important difficulties bobbing up in physics. because the checklist of references includes many papers that have been released formerly in basic terms in Russian learn journals, it may possibly additionally function a advisor to the Russian literature.

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