TY - JOUR
T1 - Global Existence and Blow-up for a Parabolic System with Nonlinear Boundary Conditions
JO - Journal of Partial Differential Equations
VL - 3
SP - 231
EP - 244
PY - 1998
DA - 1998/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5567.html
KW - Parabolic system
KW - global existence
KW - blow-up
AB -  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).