Grow-up rate of solutions for the heat equation with a sublinear source
Liangwei Wang, Jingxue Yin · Boundary Value Problems · 2012
In this paper, we investigate the grow-up rate of solutions for the heat equation with a sublinear source. We find that if the initial value grows fast enough, then it plays a major role in the growing up of solutions, while if the initial value grows slowly, then the sublinear source prevails. As a direct application of these results, we show that the effect of the sublinear source is negligible in the asymptotic behavior of solutions as if the initial value grows fast enough. MSC:35K55, 35B40.