Global existence and blow-up for a porous medium system with nonlocal boundary conditions and nonlocal sources. (English) Zbl 1263.35128

Ye, Zhuan; Xu, Xiaojing

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 82, 115-126 (2013).

Summary: This paper is devoted to a porous medium system subject to nonlocal boundary conditions and with nonlocal sources. We investigate global existence and blow-up in finite time of nonnegative solutions by using a sub-super-solution method. Moreover, under appropriate hypotheses for the conditions, we obtain asymptotic properties of the solutions.

MSC:

35K45	Initial value problems for second-order parabolic systems
74H40	Long-time behavior of solutions for dynamical problems in solid mechanics
35K65	Degenerate parabolic equations
35K59	Quasilinear parabolic equations
35B44	Blow-up in context of PDEs
35R09	Integral partial differential equations

Keywords:

porous system; nonlocal boundary conditions; nonlocal sources; global existence; finite time blow-up; sub-super-solution method; asymptotic properties