Year: 1998
Journal of Partial Differential Equations, Vol. 11 (1998), Iss. 3 : pp. 231–244
Abstract
This paper deals with the global existence and blow-up of positive solutions to the systems: u_t = ∇(u^∇u) + u¹ + v^a v_t = ∇(v^n∇v) + u^b + v^k in B_R × (0, T) \frac{∂u}{∂η} = u^αv^p, \frac{∂v}{∂η} = u^qv^β on S_R × (0, T) u(x, 0) = u_0(x), v(x, 0} = v_0(x) in B_R We prove that there exists a global classical positive solution if and only if l ≤ l, k ≤ 1, m + α ≤ 1, n + β ≤ 1, pq ≤ (1 - m - α)(1 - n - β),ab ≤ 1, qa ≤ (1 - n - β) and pb ≤ (1 - m - α).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1998-JPDE-5567
Journal of Partial Differential Equations, Vol. 11 (1998), Iss. 3 : pp. 231–244
Published online: 1998-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Parabolic system