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Matematicheskie Zametki, 2017, Volume 101, Issue 6, Pages 807–822
DOI: https://doi.org/10.4213/mzm11148 (Mi mzm11148) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On Exact Solutions of a Sobolev Equation

A. I. Aristov

Lomonosov Moscow State University
Full-text PDF (474 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm11148
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).
Received: 01.07.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 6, Pages 928–941
DOI: https://doi.org/10.1134/S0001434617050194
Bibliographic databases:
Document Type: Article
UDC: 517.955.8
Language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm11148
  • https://doi.org/10.4213/mzm11148
  • https://www.mathnet.ru/eng/mzm/v101/i6/p807
    • This publication is cited in the following 4 articles:
    1. Tahir Shahzad, Muhammad Ozair Ahmed, Muhammad Zafarullah Baber, Nauman Ahmed, Ali Akgül, Sayed M. El Din, “Novel waves structures for the nonclassical Sobolev-type equation in unipolar semiconductor with its stability analysis”, Sci Rep, 13:1 (2023)  crossref  mathscinet
    2. Abbasbandy S., Shivanian E., AL-Jizani Kh.H., “On the Analysis of a Kind of Nonlinear Sobolev Equation Through Locally Applied Pseudo-Spectral Meshfree Radial Point Interpolation”, Numer. Meth. Part Differ. Equ., 37:1 (2021), 462–478  crossref  mathscinet  isi
    3. Abdolrazaghi F., Razani A., Mirzaei R., “Multiple Weak Solutions For a Kind of Time-Dependent Equation Involving Singularity”, Filomat, 34:13 (2020), 4567–4574  crossref  mathscinet  isi
    4. A. I. Aristov, “Exact solutions of a nonclassical equation with a nonlinearity under the Laplacian”, Differ. Equ., 55:10 (2019), 1317–1327  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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