slideshow 3

Seminar on Partial Differential Equations

usually takes place each Tuesday at 09:00 in IM, rear building, ground floor
Chair: Šárka Nečasová, Milan Pokorný

A non-local diffusion equation

Nicola Zamponi
Charles University
Tuesday, 8. October 2019 - 9:00 to 10:00
We consider a non-local porous medium equation with non-local diffusion effects given by a fractional heat operator in 2 space dimensions. Global in time existence of weak solutions is shown by employing a time semi-discretization of the equations, an energy inequality, a higher integrability estimate of the approximate solution and a generalization of the well-known Div-Curl Lemma.

L^p-Strong solution to fluid-rigid body interaction system with Navier slip boundary condition

Amrita Ghosh
Institute of Mathematics, Czech Academy of Sciences
Tuesday, 1. October 2019 - 9:00 to 10:00
I will discuss the existence of a strong solution of a coupled fluid and rigid body system and the corresponding L^p-theory. Precisely, I will consider a 3D viscous, incompressible non-Newtonian fluid, containing a 3D rigid body, coupled with (non-linear) slip boundary condition at the interface and show the well-posedness of this system.

Strong maximum principle for problem involving $p$-Laplace operator

Lukáš Kotrla 
University of West Bohemia, Pilsen
Tuesday, 21. May 2019 - 9:00 to 10:00
We consider continuous nonnegative solutions to a doubly nonlinear parabolic problem with the $p$-Laplacian with zero Dirichlet boundary conditions. For simplicity we assume that both the initial data and the reaction function are continuous and nonnegative and the reaction function does not depend on $u$. We show that for $1<p<2$ the speed of propagation is infinite in the sense that for any fixed time the solution is either everywhere positive or identically zero. In particular, if the initial data are nonzero at at least one point, then for small positive time the solution is positive in the whole domain, i.e., the strong maximum principle holds. We will also apply maximum and comparison principles to problems from turbulent filtration of natural gas in porous rock and groundwater filtration in gravel. In particular, we will focus on a model of turbulent filtration of natural gas in a porous rock due to Leibenson. This is... more

Harmonic and Biharmonic Problems in Lipschitz and C^{1,1} Domains

Chérif Amrouche
University of Pau and Pays de l'Adour
Tuesday, 14. May 2019 - 9:00 to 10:00
See the attachment.