Title

Universal Self-Similarity Of Porous Media Equation With Absorption: The Critical Exponent Case

Keywords

Cauchy problem; Large time behavior; Non-linear parabolic equation; Self-similar solutions

Abstract

In this paper we study the large time behavior of non-negative solutions to the Cauchy problem of ut = Δum - uq in RN × (0, ∞), where m > 1 and q = qc ≡ m + 2/N is a critical exponent. For non-negative initial value u(x, 0) = u0(x) ∈ L1(RN), we show that the solution converges, if u0(x)(1 + x )k is bounded for some k > N, to a unique fundamental solution of ut = Δum, independent of the initial value, with additional logarithmic anomalous decay exponent in time as t[ ∞. © 2004 Elsevier Inc. All rights reserved.

Publication Date

4-10-2004

Publication Title

Journal of Differential Equations

Volume

198

Issue

2

Number of Pages

442-463

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jde.2003.10.022

Socpus ID

1642334942 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/1642334942

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