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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 12, Pages 2235–2253 (Mi zvmmf370)  
This article is cited in 2 scientific papers (total in 2 papers)

Time asymptotic behavior of the solution to a quasilinear parabolic equation

A. V. Gasnikov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
Full-text PDF (1851 kB) Citations (2)
Abstract: The time asymptotic behavior of the solution to the Cauchy problem for a quasilinear parabolic equation is analyzed. Such problems are encountered, for example, in gas dynamics and transport flow simulation. A. M. Il'in and O. A. Oleinik's well-known results are extended to a wider class of equations in which the time derivative of the unknown function is multiplied by a fixed-sign function of the former. The results have found applications in mathematical economics.
Key words: quasilinear parabolic equation, Henkin–Polterovich model with decreasing capacities, wave solution, traveling wave.
Received: 23.11.2005
Revised: 19.06.2006
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 12, Pages 2136–2153
DOI: https://doi.org/10.1134/S0965542506120128
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: A. V. Gasnikov, “Time asymptotic behavior of the solution to a quasilinear parabolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 46:12 (2006), 2235–2253; Comput. Math. Math. Phys., 46:12 (2006), 2136–2153
Citation in format AMSBIB
\Bibitem{Gas06}
\by A.~V.~Gasnikov
\paper Time asymptotic behavior of the solution to a~quasilinear parabolic equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 12
\pages 2235--2253
\mathnet{http://mi.mathnet.ru/zvmmf370}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2344969}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 12
\pages 2136--2153
\crossref{https://doi.org/10.1134/S0965542506120128}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846141780}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf370
  • https://www.mathnet.ru/eng/zvmmf/v46/i12/p2235
    • This publication is cited in the following 2 articles:
    1. Henkin G.M., “Burgers Type Equations, Gelfand's Problem and Schumpeterian Dynamics”, J. Fixed Point Theory Appl., 11:2 (2012), 199–223  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. V. Gasnikov, “Convergence in the form of a solution to the Cauchy problem for a quasilinear parabolic equation with a monotone initial condition to a system of waves”, Comput. Math. Math. Phys., 48:8 (2008), 1376–1405  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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