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Mat. Sb., 2000, Volume 191, Number 3, Pages 25–42 (Mi msb462)  

This article is cited in 2 scientific papers (total in 2 papers)

Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities

A. L. Gladkov

Vitebsk State University named after P. M. Masherov

Abstract: The Cauchy problem with non-negative continuous initial function for the equation
$$ u_t=\Delta u^m-u^p, \qquad (x,t)\in S=\mathbb R^N\times\mathbb R_+, $$
is considered for $0<p<1$, $p<m$. For generalized solutions of this problem with initial data increasing at infinity several results on their behaviour as $t\to\infty$ are established.

DOI: https://doi.org/10.4213/sm462

Full text: PDF file (303 kB)
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English version:
Sbornik: Mathematics, 2000, 191:3, 341–358

Bibliographic databases:

UDC: 517.956
MSC: 35K55, 35B40
Received: 26.01.1998 and 18.03.1999

Citation: A. L. Gladkov, “Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities”, Mat. Sb., 191:3 (2000), 25–42; Sb. Math., 191:3 (2000), 341–358

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Khramtsov, OV, “Relative stabilization of a nonlinear degenerate parabolic equation”, Differential Equations, 37:12 (2001), 1736  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    2. Prokhozhii, SA, “On the vanishing of solutions of quasilinear parabolic equations”, Differential Equations, 42:10 (2006), 1462  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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