Global existence and blow-up problems for reaction diffusion model with multiple nonlinearities

作者：Ding Juntang^*; Gao Xuyan; Li Shengjia

来源：Journal of Mathematical Analysis and Applications, 2008, 343(1): 159-169.

DOI：10.1016/j.jmaa.2008.01.038

• reaction diffusion
• multiple nonlinearities
• blow-up solutions
• global solutions

In this paper, we study the following reaction diffusion model,
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where D is a bounded domain in RN with smooth boundary partial derivative D, N >=, 2. This paper deals with interactions among three kinds of nonlinear mechanisms: nonlinear reaction, nonlinear convection and nonlinear boundary flux. The existence theorems of blow-up positive solutions, upper bound of "blow-up time," upper estimates of "blow-up rate," existence theorems of global positive solutions, and upper estimates of global positive solutions are given under suitable assumptions on a, b, c, f, g, h, r and initial data u(0)(x).

• 出版日期2008-7-1
• 单位山西农业大学