Fakulta matematiky, fyziky
a informatiky

# Seminár z kvalitatívnej teórie diferenciálnych rovníc - Jin Takahashi (12.10.2017)

## vo štvrtok 12.10.2017 o 15:00 hod. v posluchárni M/223

05. 10. 2017 23.24 hod.

Prednášajúci: Jin Takahashi (Tohoku University)

Názov prednášky: Solutions with a higher dimensional singular set for the heat equation with absorption

Termín: 12.10.2017, 15:00 hod., M/223

Abstrakt:
In this talk, we consider nonnegative solutions with a time-dependent $m$-dimensional singular set for the linear heat equation in $\mathbf{R}^n$ with an absorption term $-u^p$. Here the conditions $n-m\geq3$ and $p>1$ and some assumption on the singular set are imposed. We show that if $p\geq (n-m)/(n-m-2)$, there is no singular solution. On the other hand, in the case $p< (n-m)/(n-m-2)$, we construct two types of global-in-time singular solution. We also show the uniqueness of solutions in some class.

This is a joint work with Hikaru Yamamoto (Tokyo University of Science).

Stránka seminára