Blow-up for a non-Newton polytropic filtration system with nonlinear nonlocal source

Commun. Korean Math. Soc. 2008 Vol. 23, No. 4, 529-540 Printed December 1, 2008

Jun Zhou and Chunlai Mu Southwest University and Chongqing University

Abstract : This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system, $$u_t-\triangle_{m,p}u=u^{\alpha_1}\int_{\Omega}v^{\beta_1} (x,t)dx,\ \ v_t-\triangle_{n,q}v=v^{\alpha_2}\int_{\Omega}u^{\beta_2} (x,t)dx,$$ with homogeneous Dirichlet boundary condition. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depends on the initial data and the relations of the parameters in the system.