Global solutions and blow-up problems to a porous medium system with nonlocal sources and nonlocal boundary conditions

Abstract

Communicated by R. ShowalterThis paper deals with a porous medium system with nonlocal sources and weighted nonlocal boundary conditions. The main aim of this paper is to study how the reaction terms, the diffusion terms, and the weight functions in the boundary conditions affect the global and blow-up properties to a porous medium system. The conditions on the global existence and blow-up in finite time for nonnegative solutions are given. Furthermore, the blow-up rate estimates of the blow-up solutions are also established.

Blow-up of solutions for nonlinear parabolic equation with nonlocal source and nonlocal boundary condition

“…They established local existence, global existence and nonexistence of solutions and discussed the blow up properties of solutions. Similar results can be seen in [23,24,[26][27][28][29][30].…”