Antonín Češík
PhD student at Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University.
Working as a member of research group on Interaction of Fluids and Solids, which is led by my advisor Sebastian Schwarzacher .
Research
Analysis of a variational approach to hyperbolic problems (with S. Schwarzacher)
The aim is to investigate the properties of a variational time-discrete scheme for solving hyperbolic problems, in particular this includes dynamic evolutions of (visco-)elastic solids. The scheme is now fully discrete in time, satisfies the right energy estimates. Moreover we show the rate of convergence of this scheme to the continuous (strong) solution.
Inetrtial evolution of (visco-)elastic solids with collisions (with G. Gravina and M. Kampschulte)
arXiv:2212.00705
The aim is to extend the existence results for dynamics of (visco-)elastic solids past the time of a (self-)collision. In particular, we assume only the non-interpenetrability of the solid, and our construciton directly provides the physically correct contact forces. In particular, the contact force constructed as a Lagrange multiplier in fact turns out to be vector-valued measure, supported at the points of contact and normal to the boundary.
Convex hull properties for parabolic systems of PDE (master thesis)
The thesis investigates a generalisation of the maximum principles for PDE into the context of systems of PDE - the convex hull property. The main novelty is a proof of convex hull property for the parabolic p-Laplacian.