Abstract and Applied Analysis

Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source

Abstract

We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ${u}_{t}=div(|\nabla {u}^{m}{|}^{p-2}\nabla {u}^{l})+{u}^{q},\mathrm{ }(x$ $,t)\in {R}^{N}×(0,T)$, where $N\ge 1$, $p>2$ , and $m$, $l$,$\mathrm{ }q>1$, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. Moreover, under some suitable conditions we prove single-point blow-up for a large class of radial decreasing solutions.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 109546, 19 pages.

Dates
First available in Project Euclid: 4 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365099933

Digital Object Identifier
doi:10.1155/2012/109546

Mathematical Reviews number (MathSciNet)
MR2947766

Zentralblatt MATH identifier
1250.35045

Citation

Zheng, Pan; Mu, Chunlai; Liu, Dengming; Yao, Xianzhong; Zhou, Shouming. Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 109546, 19 pages. doi:10.1155/2012/109546. https://projecteuclid.org/euclid.aaa/1365099933

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