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

The Fractional Calderon problem

Tuhin Ghosh
Hong Kong University of Science and Technology
Tuesday, 17. December 2019 - 10:15 to 11:15
We will be discussing the fractional Calderon problem, where one tries to determine an unknown potential in a fractional Schrodinger equation from the exterior measurements of solutions.

Compressible nonlinearly viscous fluids: Asymptotic analysis in a 3D curved domain

Richard Andrášik
Palacký University Olomouc
Tuesday, 17. December 2019 - 9:00 to 10:00
Governing equations representing mathematical description of continuum mechanics have often three spatial dimensions and one temporal dimension. However, their analytical solution is usually unattainable, and numerical approximation of the solution unduly complicated and computationally demanding. Thus, these models are frequently simplified in various ways. One option of a simplification is a reduction of the number of spatial dimensions. Nonsteady Navier-Stokes equations for compressible nonlinearly viscous fluids in a three-dimensional domain were considered. These equations need a simplification, when possible, to be effectively solved. Therefore, a dimension reduction was performed for this type of a model. Dynamics of a compressible fluid in thin domains was studied. The current framework was extended by dealing with nonsteady Navier-Stokes equations for compressible nonlinearly viscous fluids in a deformed three-dimensional domain where only two dimensions are dominant. The... more

Influence of rheological parameters on generalized Oldroyd-B fluid flow through curved pipes

Marília Pires
Institute of Mathematics, CAS
Tuesday, 10. December 2019 - 9:00 to 10:00
Flows in curved pipes are very challenging and considerably more complex than flows in straight pipes. Due to fluid inertia, a secondary motion appears in addition to the primary axial flow. It is induced by an imbalance between the cross stream pressure gradient and the centrifugal force and consists of a pair of counter-rotating vortices, which appear even for the most mildly curved pipe.

Parallel to the pipe curvature ratio, the rheological parameters of the fluid have a considerable influence on the flow behavior. In this work, numerical simulations obtained by finite elements method, involving steady, incompressible, creeping and inertial flows of the generalized Oldroyd-B fluid  through curved pipes are presented. The behavior of the solutions is discussed with respect to different rheologic and geometric flow parameters.

Chemotaxis-consumption model and the importance of the boundary conditions

Marcel Braukhoff
Vienna University of Technology
Tuesday, 26. November 2019 - 10:15 to 11:15
In the talk we discuss the behavior of the concentration of some bacteria swimming in water (for example of the species Bacillus subtilis), whose otherwise random motion is partially directed towards higher concentrations of a signaling substance (oxygen) they consume. After a transition phase, the system can be described using a chemotaxis-consumption model on a bounded domain. Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been experimentally observed.

Following the suggestions that the main reason for that is usage of inappropriate boundary conditions, this talks considers no-flux boundary conditions for the bacteria density and the physically meaningful Robin boundary conditions for the signaling substance and Dirichlet boundary... more