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

Title & Authors
CRITICAL BLOW-UP AND EXTINCTION EXPONENTS FOR NON-NEWTON POLYTROPIC FILTRATION EQUATION WITH SOURCE
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 $\small{q_1,\;q_2\;{\in}\;(0,+{\infty})}$) with $\small{q_1\;{<}\;q_2}$. In other words, when q belongs to different intervals (0, $\small{q_1),\;(q_1,\;q_2),\;(q_2,+{\infty}}$), 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, $\small{q_2}$]. However, when q $\small{{\in}\;(q_2,+{\infty}}$), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval ($\small{q_1,+{\infty}}$), while for q $\small{{\in}\;(0,\;q_1}$), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q
Keywords
non-Newtonian polytropic equation;critical blow-up exponent;critical extinction exponent;
Language
English
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