Uniform blow-up rate for parabolic equations with a weighted nonlocal nonlinear source

作者：Jiang, Liangjun^*; Xu, Yongping

来源：Journal of Mathematical Analysis and Applications, 2010, 365(1): 50-59.

DOI：10.1016/j.jmaa.2009.10.004

• Semi-linear diffusion equation
• Uniform blow-up rate
• Nonlocal sources
• Weight function

In this paper, the blow-up rate of solutions of semi-linear reaction-diffusion equations with a more complicated Source term, which is a product of nonlocal (or localized) source and weight function a(x), is investigated. It is proved that the solutions have global blow-up, and that the rates of blow-up are uniform in all compact subsets of the domain. Furthermore, the blow-up rate of vertical bar u(t)vertical bar(infinity) is precisely determined.

• 出版日期2010-5-1
• 单位南京林业大学; 南京晓庄学院