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Matematicheskie Zametki, 2017, Volume 102, Issue 1, Pages 6–16
DOI: https://doi.org/10.4213/mzm11478 (Mi mzm11478) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On a Nonlinear Third-Order Equation

A. I. Aristov

Lomonosov Moscow State University
Full-text PDF (454 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm11478
Abstract: A nonclassical nonlinear third-order partial differential equation modeling nonstationary processes in a semiconductor medium is studied. Seven classes of exact solutions of this equation given as explicit, implicit, and quadrature formulas are constructed. It is shown that, among these solutions, there are some bounded globally with respect to time and some approaching infinity on finite time intervals. These results are of interest in view of the following property of initial boundary-value problems for the given equation. Here the method of energy estimates used in many papers to justify the boundedness or unboundedness of solutions does not provide sufficient conditions for the unboundedness of solutions on finite time intervals.
Keywords: nonlinear partial differential equations, blow-up of solutions, exact solutions.
Received: 05.12.2016
English version:
Mathematical Notes, 2017, Volume 102, Issue 1, Pages 3–11
DOI: https://doi.org/10.1134/S000143461707001X
Bibliographic databases:
Document Type: Article
UDC: 517.955.8
Language: Russian
Citation: A. I. Aristov, “On a Nonlinear Third-Order Equation”, Mat. Zametki, 102:1 (2017), 6–16; Math. Notes, 102:1 (2017), 3–11
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11478
  • https://www.mathnet.ru/eng/mzm/v102/i1/p6
    • This publication is cited in the following 1 articles:
    1. A. I. Aristov, “Exact solutions of a nonclassical equation with a nonlinearity under the Laplacian”, Differ. Equ., 55:10 (2019), 1317–1327  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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