Similar solutions and the asymptotics of filtration equations
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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 ⩼φ(u) is “close” to uλ for small u.
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