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Critical exponent for non‐Newtonian filtration equation with homogeneous Neumann boundary data
Author(s) -
Wang Zejia,
Yin Jingxue,
Wang Lusheng
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.955
Subject(s) - mathematics , exponent , critical exponent , fujita scale , mathematical analysis , neumann boundary condition , homogeneous , non newtonian fluid , boundary (topology) , mathematical physics , thermodynamics , scaling , combinatorics , physics , geometry , philosophy , linguistics , meteorology
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 . Copyright © 2007 John Wiley & Sons, Ltd.