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Critical exponent for non-Newtonian filtration equation with homogeneous Neumann boundary data

✍ Scribed by Zejia Wang; Jingxue Yin; Lusheng Wang

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
101 KB
Volume
31
Category
Article
ISSN
0170-4214

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✦ Synopsis

This paper is concerned with large time behavior of solutions to the homogeneous Neumann problem of the non-Newtonian filtration equation. It is shown that the critical Fujita exponent for the problem considered is determined not only by the spatial dimension and the nonlinearity exponent, but also by the coefficient k of the first-order term. In fact, we show that there exist two thresholds k ∞ and k 1 on the coefficient k of the first-order term, and the critical Fujita exponent is a finite number when k is between k ∞ and k 1 , while the critical exponent does not exist when k k ∞ or k k 1 .

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