CRITICAL BLOW-UP AND EXTINCTION EXPONENTS FOR NON-NEWTON POLYTROPIC FILTRATION EQUATION WITH SOURCE

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 6, 2009, pp.1159-1173
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.6.1159

Title & Authors

CRITICAL BLOW-UP AND EXTINCTION EXPONENTS FOR NON-NEWTON POLYTROPIC FILTRATION EQUATION WITH SOURCE

Zhou, Jun; Mu, Chunlai;

Zhou, Jun; Mu, Chunlai;

Abstract

This paper deals with the critical blow-up and extinction exponents for the non-Newton polytropic filtration equation. We reveals a fact that the equation admits two critical exponents ) with . In other words, when q belongs to different intervals (0, ), the solution possesses complete different properties. More precisely speaking, as far as the blow-up exponent is concerned, the global existence case consists of the interval (0, ]. However, when q ), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval (), while for q ), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q = is concerned, the other parameter will play an important role. In other words, when belongs to different interval (0, ) or (,+), where is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely different properties.

Keywords

non-Newtonian polytropic equation;critical blow-up exponent;critical extinction exponent;

Language

English

Cited by

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