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GLOBAL EXISTENCE AND BLOW-UP FOR A NON-NEWTON POLYTROPIC FILTRATION SYSTEM WITH NONLOCAL SOURCE

Part of: Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  01 July 2008

JUN ZHOU  and
CHUNLAI MU
JUN ZHOU*
Affiliation:
School of Mathematics and Physics, Chongqing University, Chongqing, 400044, People’s Republic of China (email: [email protected])
CHUNLAI MU
Affiliation:
School of Mathematics and Physics, Chongqing University, Chongqing, 400044, People’s Republic of China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system with nonlocal source, Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depending on the initial data and the relations between αβ and mn(p−1)(q−1). In the special case, α=n(q−1), β=m(p−1), we also give a criteria for the solution to exist globally or blow up in finite time, which depends on a,b and ζ(x),ϑ(x) as defined in our main results.

Keywords

non-Newtonian polytropic systemnonlocal sourceglobal existenceblow-up

MSC classification

Secondary: 35K65: Degenerate parabolic equations 35B33: Critical exponents
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 1 , July 2008 , pp. 13 - 29
Copyright
Copyright © Australian Mathematical Society 2009

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