Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data

Amy Poh Ai Ling; Masahiko Shimojō

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 3, page 287-297
  • ISSN: 0862-7959

Abstract

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We consider solutions of quasilinear equations u t = Δ u m + u p in ℝ N with the initial data u 0 satisfying 0 < u 0 < M and lim | x | → ∞ 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 ℝ N when m > p > 1 .

How to cite

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Ling, Amy Poh Ai, and Shimojō, Masahiko. "Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data." Mathematica Bohemica 144.3 (2019): 287-297. <http://eudml.org/doc/294294>.

@article{Ling2019,
abstract = {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 $\lim _\{|x|\rightarrow \infty \}u_\{0\}(x)=M$ 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 $m>p>1$.},
author = {Ling, Amy Poh Ai, Shimojō, Masahiko},
journal = {Mathematica Bohemica},
keywords = {quasilinear heat equation; total blow-up; blow-up only at space infinity},
language = {eng},
number = {3},
pages = {287-297},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data},
url = {http://eudml.org/doc/294294},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Ling, Amy Poh Ai
AU - Shimojō, Masahiko
TI - Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 3
SP - 287
EP - 297
AB - 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 $\lim _{|x|\rightarrow \infty }u_{0}(x)=M$ 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 $m>p>1$.
LA - eng
KW - quasilinear heat equation; total blow-up; blow-up only at space infinity
UR - http://eudml.org/doc/294294
ER -

References

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