Global existence and blow-up of solutions to an evolution p-Laplace system coupled via nonlocal sources

作者：Wu Xuesong^*; Gao Wenjie

来源：Journal of Mathematical Analysis and Applications, 2009, 358(2): 229-237.

DOI：10.1016/j.jmaa.2009.04.059

• Nonlinear boundary value problem
• Evolution p-Laplacian
• Global existence
• Blow-up
• Nonlocal source

The aim of this paper is to investigate the behavior of positive solutions to the following system of evolution p-Laplace equations coupled via nonlocal Sources:
{u(t) = (vertical bar u(x)vertical bar(p1-1) u(x))(x) + integral(a)(0) v(m1) (xi, t)d xi, (x, t) in [0, a] x (0, T)
v(t) = (vertical bar v(x)vertical bar(p2-1) v(x))(x) + integral(a)(0) u(m2) (xi, t)d xi, (x, t) in [0, a] x (0, T)
with nonlinear boundary conditions u(x)vertical bar(x=0) = 0, u(x)vertical bar(x=a) =u(q11) v(q12)vertical bar(x=a,) v(x)vertical bar(x)=0 =0, v(x)vertical bar(x)=a = u(q21) v(q22)vertical bar(x=a) and the initial data (u(0), v(0)), where p(1), p(2) > 1, m(1), m2, q(11), q(12), q(21), q(22) > 0. Under appropriate hypotheses, the authors first prove a local existence result by a regularization method. Then the authors discuss the global existence and blow-up of positive weak solutions by using a comparison principle.

• 出版日期2009-10-15
• 单位吉林大学