A nonlinear diffusion system coupled via nonlinear boundary flux

作者：Mi Yongsheng^*; Mu Chunlai; Chen Botao

来源：Journal of Mathematical Analysis and Applications, 2011, 376(2): 613-624.

DOI：10.1016/j.jmaa.2010.10.065

• Global existence curve
• Nonlinear diffusion system
• M-matrix
• Nonlinear boundary flux
• Blow-up

In this paper, we deal with the global existence and nonexistence of solutions to a nonlinear diffusion system coupled via nonlinear boundary flux. 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 Wang et al. [Nonlinear Anal. 71 (2009) 2134-2140] and Li et al. U. Math. Anal. Appl. 340 (2008) 876-883] to more general equations.

• 出版日期2011-4-15
• 单位长江师范学院; 重庆大学