Universal self-similarity of porous media equation with absorption: the critical exponent case

    Authors

    Y. W. Qi;X. D. Liu

    Comments

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    Abbreviated Journal Title

    J. Differ. Equ.

    Keywords

    large time behavior; non-linear parabolic equation; Cauchy problem; self-similar solutions; LARGE TIME BEHAVIOR; NONLINEAR PARABOLIC EQUATIONS; ASYMPTOTIC-BEHAVIOR; Mathematics

    Abstract

    In this paper we study the large time behavior of non-negative solutions to the Cauchy problem of u(t) = Deltau(m) - u(q) in R-N x (0, infinity), where m > 1 and q = q(c) equivalent to m + 2/N is a critical exponent. For non-negative initial value u(x, 0) = u(0) (x) is an element of L-1 (R-N), we show that the solution converges, if u(0) (x) (1 + \x\)(k) is bounded for some k > N, to a unique fundamental solution of u(t) = Deltau(m), independent of the initial value, with additional logarithmic anomalous decay exponent in time as t -- > infinity. (C) 2004 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Differential Equations

    Volume

    198

    Issue/Number

    2

    Publication Date

    1-1-2004

    Document Type

    Article

    Language

    English

    First Page

    442

    Last Page

    463

    WOS Identifier

    WOS:000220096700009

    ISSN

    0022-0396

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