Advances in Differential Equations

Instantaneous support shrinking phenomenon in the case of fast diffusion for a doubly nonlinear parabolic equation with absorption

S. P. Degtyarev

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Abstract

We study the instantaneous support shrinking phenomenon for a doubly nonlinear parabolic equation in the fast diffusion case. The initial data of the Cauchy problem are locally finite Radon measures. We obtain for nonnegative solutions necessary and sufficient condition for instantaneous support shrinking phenomenon in terms of local behavior of the initial data. In the same terms we express sharp with respect to rate bilateral estimates for the size of the support.

Article information

Source
Adv. Differential Equations Volume 13, Number 11-12 (2008), 1031-1050.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867285

Mathematical Reviews number (MathSciNet)
MR2483129

Zentralblatt MATH identifier
1185.35132

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B40: Asymptotic behavior of solutions 35K65: Degenerate parabolic equations

Citation

Degtyarev, S. P. Instantaneous support shrinking phenomenon in the case of fast diffusion for a doubly nonlinear parabolic equation with absorption. Adv. Differential Equations 13 (2008), no. 11-12, 1031--1050. https://projecteuclid.org/euclid.ade/1355867285.


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