Asymptotic behavior of solutions to coupled porous medium systems with boundary degeneracy

Abstract

This article concerns the asymptotic behavior of solutions of one-dimensional porous medium systems with boundary degeneracy in bounded and unbounded intervals. It is shown that the degree of the boundary degeneracy and the exponent of the nonlinear diffusion determine asymptotic behaviors of solutions. For the problem in a bounded interval, if the degeneracy is not strong, the problem admits both nontrivial global and blowing-up solutions, while if the degeneracy is strong enough, any nontrivial solution to the problem must blow up in a finite time. For the problem in an unbounded interval, the Fujita type blowing-up theorems are established and the critical Fujita exponent is formulated by the degree of the boundary degeneracy and the exponent of nonlinear diffusion.