Global Existence and Blow-up for a Parabolic System with Nonlinear Boundary Conditions

Global Existence and Blow-up for a Parabolic System with Nonlinear Boundary Conditions

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).

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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