Seminar 2.3.2023: Petra Mackova

[quittner]

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Štvrtok 6.10.2022 o 14:00, poslucháreň M-223

Petra Macková (KAMŠ FMFI UK):
Fast diffusion equation: uniqueness of solutions with a moving singularity

Abstrakt:
This talk focuses on open questions in the area of the uniqueness
of distributional solutions of the fast diffusion equation
with a given source term. Assuming that the source term is a measure,
the existence of different classes of solutions is known,
however, their uniqueness is an open problem.
The existence of a class of asymptotically radially symmetric solutions
with a singularity that moves along a prescribed curve was proved
by M. Fila, J. Takahashi, and E. Yanagida. More recently, it has been
established by M. Fila, P. M., J. Takahashi, and E. Yanagida that these
solutions solve the corresponding problem with a moving Dirac source term.
In this talk, we discuss the uniqueness of these solutions.
This is a joint work with M. Fila.