Affiliation:
1. Lomonosov Moscow State University
Abstract
It is a brief exposition of results of the investigation of Cauchy problem for some nonlinear equation of
pseudoparabolic type that is a generalisation of some model of semiconductor theory. In the paper, the
potential theory for the linear part of the equation is elaborated, which demanded quite intricate technique, which can be used in other equations. The properties of the fundamental solution of this linear part are also
of interest, because of the singularity of its 1st time derivative. This is not usual for this type of equations.
Also, we obtain sufficiant conditions of solvability and of finite-time blow-up.
Funder
Russian Science Foundation
Subject
Space and Planetary Science,General Physics and Astronomy,Astronomy and Astrophysics
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