Volume 11, Issue 3
Global Existence and Blow-up for a Parabolic System with Nonlinear Boundary Conditions

Zhigui Lin

DOI:

J. Part. Diff. Eq., 11 (1998), pp. 231-244.

Published online: 1998-11

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  • 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).

  • Keywords

Parabolic system global existence blow-up

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@Article{JPDE-11-231, author = {}, title = {Global Existence and Blow-up for a Parabolic System with Nonlinear Boundary Conditions}, journal = {Journal of Partial Differential Equations}, year = {1998}, volume = {11}, number = {3}, pages = {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).}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5567.html} }
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).
Zhigui Lin . (2019). Global Existence and Blow-up for a Parabolic System with Nonlinear Boundary Conditions. Journal of Partial Differential Equations. 11 (3). 231-244. doi:
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