Faculty of Mathematics, Physics
and Informatics
Comenius University in Bratislava

Seminar on Qualitative Theory of Differential Equations - Petra Macková (15.10.2020)

Thursday 15.10.2020 at 14:00, Lecture room C

05. 10. 2020 19.46 hod.
By: Pavol Quittner

Petra Macková:
Solutions with moving singularities for nonlinear diffusion equations

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.

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