|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
On blow up rate for sign-changing solutions in a convex domain
| Title: | On blow up rate for sign-changing solutions in a convex domain |
| Authors: | Giga, Y. Browse this author | | Matsui, S. Browse this author | | Sasayama, S. Browse this author |
| Issue Date: | Jul-2003 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 594 |
| Start Page: | 1 |
| End Page: | 12 |
| Abstract: | This paper studies a growth rate of a solution blowing up at time T of the semilinear heat equation Ut - £:iu - lulP-1u = 0 in a convex domain D in Rn with zero-boundary condition. For a subcritical p E (1, (n + 2)/(n - 2)) a growth rate estimate lu(x, t)I :S C(T- t)-1/(p-l), x E D, t E (0, T) is established with C independent oft provided that D is uniformly 02. The estimate applies to sign-changing solutions. The same estimate has been recently established when D = Rn by authors. The proof is similar but we need to establish Lh - Lk estimate for a time-dependent domain because of the presence of the boundary. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69343 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
|
Submitter: 数学紀要登録作業用
|
