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Mat. Zametki, 2017, Volume 101, Issue 6, Pages 807–822 (Mi mz11148)  

On Exact Solutions of a Sobolev Equation

A. I. Aristov

Lomonosov Moscow State University

Abstract: A nonlinear Sobolev-type equation that can be used to describe nonstationary processes in the semiconductor medium is studied. A number of families of exact solutions of this equation that can be expressed in terms of elementary functions and quadratures is obtained; some of these families contain arbitrary sufficiently smooth functions of one argument. The qualitative behavior of the resulting solutions is analyzed.

Keywords: Sobolev space, nonlinear differential equation, algebraic and differential nonlinearities, blow-up of a solution.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation МК-6108.2015.9
This work was supported by the Grant of the President of the Russian Federation for Young Russian Scientists Awarded the Title of Candidate of Science (grant no. MK-6108.2015.9).


DOI: https://doi.org/10.4213/mzm11148

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English version:
Mathematical Notes, 2017, 101:6, 928–941

Bibliographic databases:

UDC: 517.955.8
Received: 01.07.2016

Citation: A. I. Aristov, “On Exact Solutions of a Sobolev Equation”, Mat. Zametki, 101:6 (2017), 807–822; Math. Notes, 101:6 (2017), 928–941

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