Extinction of solutions to a class of fast diffusion systems with nonlinear sources

2013/12/21 by Han, Yuzhu, Gao, Wenjie
#35K40 #35K51 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.6243

Abstract

In this paper, the finite time extinction of solutions to the fast diffusion system u_t=div(|∇ u|^p-2∇ u)+v^m, v_t=div(|∇ v|^q-2∇ v)+uⁿ is investigated, where 10 and Ω⊂ ℝ^N (N≥1) is a bounded smooth domain. After establishing the local existence of weak solutions, the authors show that if mn>(p-1)(q-1), then any solution vanishes in finite time provided that the initial data are ``comparable"; if mn=(p-1)(q-1) and Ω is suitably small, then the existence of extinction solutions for small initial data is proved by using the De Giorgi iteration process and comparison method. On the other hand, for 1

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