抄録
In this paper, we consider a quasi-linear parabolic equation ut= up(xxx+ u) . It is known that there exist blow-up solutions and some of them develop Type II singularity. However, only a few results are known about the precise behavior of Type II blow-up solutions for p> 2 . We investigated the blow-up solutions for the equation with periodic boundary conditions and derived upper estimates of the blow-up rates in the case of 2 < p< 3 and in the case of p= 3 , separately. In addition, we assert that if 2 ≤ p≤ 3 then limt↗T(T-t)1p+εmaxu(x,t)=0 z for any ε> 0 under some assumptions.
| 本文言語 | English |
|---|---|
| ページ（範囲） | 381-405 |
| ページ数 | 25 |
| ジャーナル | Japan Journal of Industrial and Applied Mathematics |
| 巻 | 41 |
| 号 | 1 |
| DOI | |
| 出版ステータス | Published - 1月 2024 |