Seminár z kvalitatívnej teórie diferenciálnych rovníc - Petra Macková (26.11.2020)
vo štvrtok 26.11.2020 o 14:00 hod. online formou
Od: Pavol Quittner
Prednášajúci: Petra Macková
Názov prednášky: Solutions with moving singularities for nonlinear diffusion equations
Termín: 26.11.2020, 14:00 hod., MS Teams
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. It turns out that there appears a critical exponent for the existence of such solutions. I will give a sketch of the proof of the existence of such solutions, which is based on finding suitable sub- and supersolutions.