| Title:
|
Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data (English) |
| Author:
|
Ling, Amy Poh Ai |
| Author:
|
Shimojō, Masahiko |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
144 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
287-297 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider solutions of quasilinear equations $u_{t}=\Delta u^{m} + u^{p}$ in $\mathbb R^{N}$ with the initial data $u_{0}$ satisfying $0 < u_{0}< M$ and $\lim _{|x|\to \infty }u_{0}(x)=M$ for some constant $M>0$. It is known that if $0<m<p$ with $p>1$, the blow-up set is empty. We find solutions $u$ that blow up throughout $\mathbb R^{N}$ when $m>p>1$. (English) |
| Keyword:
|
quasilinear heat equation |
| Keyword:
|
total blow-up |
| Keyword:
|
blow-up only at space infinity |
| MSC:
|
35B44 |
| MSC:
|
35K59 |
| idZBL:
|
Zbl 07088852 |
| idMR:
|
MR3985858 |
| DOI:
|
10.21136/MB.2018.0026-18 |
| . |
| Date available:
|
2019-07-24T11:11:53Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147775 |
| . |
| Reference:
|
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| Reference:
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