Global existence and nonexistence of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions

作者：Mi Yongsheng^*; Mu Chunlai; Li Zhongping

来源：Applicable Analysis, 2010, 89(12): 1789-1803.

DOI：10.1080/00036811.2010.495337

• global existence curve
• degenerate parabolic systems
• M-matrix
• nonlinear boundary flux
• blow-up

In this article, we deal with the global existence and nonexistence of solutions to the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions. By constructing various kinds of sub-and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions. The critical curve of Fujita type is conjectured with the aid of some new results, which extend the recent results of Zheng, Song, and Jiang [Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux, J. Math. Anal. Appl. 298 (2004), pp. 308-324], Zhou and Mu [Critical curve for a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux, Nonlinear Anal. 68 (2008), pp. 1-11], and Zhou and Mu [Algebraic criteria for global existence or blow-up for a boundary coupled system of nonlinear diffusion equations, Appl. Anal. 86 (2007), pp. 1185-1197] to more general equations.

• 出版日期2010
• 单位长江师范学院; 重庆大学