Similar solutions and the asymptotics of filtration equations

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School of Mathematical Sciences

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Abstract

In this paper we consider the asymptotic behavior of solutions of the quasilinear equation of filtration as t→∞. We prove that similar solutions of the equation u_t = (u^λ)_xx asymptotically represent solutions of the Cauchy problem for the full equation u_t = [φ(u)]_xx if {greater-than with question mark above}φ(u) is "close" to u^λ for small u.

Original language	English
Pages (from-to)	171-183
Number of pages	13
Journal	Archive for Rational Mechanics and Analysis
Volume	60
Issue number	2
DOIs	https://doi.org/10.1007/BF00250678
State	Published - Jun 1976

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10.1007/BF00250678

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title = "Similar solutions and the asymptotics of filtration equations",

abstract = "In this paper we consider the asymptotic behavior of solutions of the quasilinear equation of filtration as t→∞. We prove that similar solutions of the equation ut = (uλ)xx asymptotically represent solutions of the Cauchy problem for the full equation ut = [φ(u)]xx if {greater-than with question mark above}φ(u) is {"}close{"} to uλ for small u.",

author = "Kamenomostskaya, {S. Kamin}",

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Similar solutions and the asymptotics of filtration equations

Abstract

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