Seminar 5.3.2020: Jin Takahashi
Posted: Fri Feb 21, 2020 10:51 am
Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations
Thursday 5.3.2020 at 14:00 Lecture room M-223
Jin Takahashi (Tokyo Institute of Technology):
Existence of solutions with moving singularities
for a semilinear heat equation with a critical exponent
Abstract:
We consider nonnegative singular solutions of a superlinear heat equation $u_t -\Delta u=u^p$ on $\mathbf{R}^N$.
Sato-Yanagida (2009) showed the existence of solutions with moving singularities in the case $N/(N-2)<p<p_{JL}^*$,
where $p_{JL}^*$ is an explicit exponent. Kan-T. (2017) studied the case $p<N/(N-2)$.
In this talk, we construct a solution with an explicit moving singularity in a critical case $p=N/(N-2)$.
In the context of the uniqueness of mild solutions, our result refines counter examples given by Terraneo (2002)
in view of pointwise behavior.
Seminar on Qualitative Theory of Differential Equations
Thursday 5.3.2020 at 14:00 Lecture room M-223
Jin Takahashi (Tokyo Institute of Technology):
Existence of solutions with moving singularities
for a semilinear heat equation with a critical exponent
Abstract:
We consider nonnegative singular solutions of a superlinear heat equation $u_t -\Delta u=u^p$ on $\mathbf{R}^N$.
Sato-Yanagida (2009) showed the existence of solutions with moving singularities in the case $N/(N-2)<p<p_{JL}^*$,
where $p_{JL}^*$ is an explicit exponent. Kan-T. (2017) studied the case $p<N/(N-2)$.
In this talk, we construct a solution with an explicit moving singularity in a critical case $p=N/(N-2)$.
In the context of the uniqueness of mild solutions, our result refines counter examples given by Terraneo (2002)
in view of pointwise behavior.