Asymptotic analysis to blow-up points for the porous medium equation with a weighted non-local source

作者：Zhou Jun^*; Mu Chunlai

来源：APPLICABLE ANALYSIS, 2009, 88(1): 111-120.

DOI：10.1080/00036810802713792

• asymptotic analysis
• porous medium equation
• non-linear non-local source
• blow-up set
• global blow-up
• single blow-up
• weight source

This article deals with the porous medium equation with a more complicated source term, [image omitted] subject to the homogeneous Dirichlet condition, where [image omitted] is a ball with radius R, m 1 and the non-negative constants [image omitted] satisfying [image omitted]. We investigate how the three factors (the non-local source [image omitted], the local source [image omitted] and the weight function a(x)) influence the asymptotic behaviour of the solutions. It is proved that (i) when p 1, the non-local source plays a dominating role, i.e. the blow-up set of the system is the whole domain BR,a, where [image omitted]. (ii) When p m, this system presents single blow-up patterns. In other words, the local term dominates the non-local term in the blow-up profile. Moreover, the blow-up rate estimate is established with more precise coefficients determined.

• 出版日期2009
• 单位重庆大学; 西南大学