If you are interested in writing your bachelor/diploma thesis in the matematical modelling group or with researchers collaborating the mathematical modelling group, you are most welcome. Below you will find a list of topics offered by the members of the group and some of our collaborators. In general we are ready to discuss the choice of bachelor/master with you, and we are willing to search for a topic that will suit your needs. If you want to work with someone in the mathematical modelling group, please do not be shy, and contact him or her directly even if he or she is currently offering no thesis topics.

Last update: **1st November 2017**

Bachelor thesis:

- Godunov description of solids (Michal Pavelka)
- Simplified non-equilibrium thermodynamic modeling of polymeric foams (Michal Pavelka)
- Thermodynamic modelling of zinc-air flow battery (Michal Pavelka)
- On counterexamples of weak solvability to the problem div u = f (Milan Pokorný)
- Solution to the problem div u = f in domains with noncompact boundaries (Milan Pokorný)
- Existence and smoothness of solution to Laplace problem for several boundary in smooth and nonsmooth domains (Miroslav Bulíček)
- Sobolev spaces of non-integer order (Miroslav Bulíček)
- Jump conditions and dynamic surface tension at non-material interfaces (Ondřej Souček)

Master thesis:

- Optimization of colloid suspension modeling (Michal Pavelka)
- Non-equilibrium thermodynamic modeling of polymeric foams (Michal Pavelka)
- Non-equilibrium thermodynamics of solids and fluids (Michal Pavelka)
- Generalised solutions to equations of fluid mechanics (Eduard Feireisl) The work will be focused on equations of fluid mechanics such as the Euler equations and Navier-Stokes equations. Generalised solution is understood as the weak solution or a solution in the sense of Young measures. Student can investigate the concepts of the solution, their applications in numerical analysis and in the study of singular limits.
- Modelling of barotropic oceanic currents on a sphere with time dependent ocean area geometry (Zdeněk Martinec)
- Compressible Navier-Stokes-Fourier system for the limit value of the adiabatic constant (Milan Pokorný)
- Analysis of the numerical solution of Forcheimer model (Vít Dolejší)
- Regularity of solution to simplified turbulence models (Miroslav Bulíček)
- Mathematical analysis of models with implicitly bounded linearized strain tensor (Miroslav Bulíček)
- On convergence of finite element method for elliptic equations in the space of contiuous functions (Miroslav Bulíček)
- Application of the spectral method to the simulation of the phase-field model for martensitic transformation (Karel Tůma)
- Non-uniform thin-shell theory – a numerical study of the approximation’s applicability in planetary sciences (Ondřej Souček)
- Modeling of thermal convection in icy satellites with the inclusion of grain-growth evolution (Ondřej Souček)
- Mimetic finite differences (Jaroslav Hron) Implementation and testing of this numerical method. Please contact me for further details.
- Fluid structure interaction with application in the modelling of flow through aortic valves (Jaroslav Hron) Continuation of a long term research project in collaboration with medical doctors. Please contact me for further details.
- Microfluidics (Jaroslav Hron) Please contact me for further details.