Abstract:
We consider the Cauchy problem with a non-negative continuous initial function for the equation
ut=(um)xx+c(un)x,
where m>1, m⩾n⩾1 and c is a positive constant. We prove a number of existence and uniqueness theorems for generalized solutions increasing at infinity for this Cauchy problem; we also investigate the behaviour of these solutions for large values of the time.
Citation:
A. L. Gladkov, “The Cauchy problem in classes of increasing functions for the equation of filtration with convection”, Sb. Math., 186:6 (1995), 803–825
\Bibitem{Gla95}
\by A.~L.~Gladkov
\paper The Cauchy problem in classes of increasing functions for the~equation of filtration with convection
\jour Sb. Math.
\yr 1995
\vol 186
\issue 6
\pages 803--825
\mathnet{http://mi.mathnet.ru/eng/sm44}
\crossref{https://doi.org/10.1070/SM1995v186n06ABEH000044}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1349013}
\zmath{https://zbmath.org/?q=an:0841.35056}
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Linking options:
https://www.mathnet.ru/eng/sm44
https://doi.org/10.1070/SM1995v186n06ABEH000044
https://www.mathnet.ru/eng/sm/v186/i6/p35
This publication is cited in the following 7 articles:
Habeeb A. Aal-Rkhais, Ruba H. Qasim, “Asymptotic behaviour for a parabolic p-Laplacian equation with an advection force”, J. Phys.: Conf. Ser., 2701:1 (2024), 012120
Mykola Bokalo, Oleh Buhrii, Nikolyetta Hryadil, “Initial–boundary value problems for nonlinear elliptic–parabolic equations with variable exponents of nonlinearity in unbounded domains without conditions at infinity”, Nonlinear Analysis, 192 (2020), 111700
Prokhozhii, SA, “On the vanishing of solutions of quasilinear parabolic equations”, Differential Equations, 42:10 (2006), 1462
Khramtsov O., “Relative Stabilization of Solutions of a Degenerating Parabolic Equation with Nonlinear Lower-Order Terms”, Differ. Equ., 40:11 (2004), 1638–1644
A. L. Gladkov, “Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities”, Sb. Math., 191:3 (2000), 341–358
Daniele Andreucci, “Degenerate parabolic equations with initial data measures”, Trans. Amer. Math. Soc., 349:10 (1997), 3911
Gladkov A., “The Cauchy Problem for the Porous Medium Equation with Strong Convection in Infinity”, Dokl. Akad. Nauk Belarusi, 40:6 (1996), 27–30
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