Seminar 26.11.2020: Petra Mackova

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 26.11.2020: Petra Mackova

Postby quittner » Mon Oct 05, 2020 4:43 pm

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

Thursday 26.11.2020 at 14:00

Petra Macková (KAMŠ FMFI UK):
Solutions with moving singularities for nonlinear diffusion equations

MS-Teams link:
https://teams.microsoft.com/l/meetup-jo ... 0ff7%22%7d

Abstract:
There are various results on solutions with moving singularities for the heat equation,
semilinear heat equations, or the Navier-Stokes system.
This talk will be concerned with the existence of positive solutions of equations
of porous medium type with a singularity that moves in time along a prescribed curve
and keeps the spatial profile of singular stationary solutions,
which have a substantially different form in two space dimensions and dimensions higher than two.
I will give a sketch of the proof of the existence of such solutions,
which is based on finding suitable sub- and supersolutions.
quittner
 
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