Dr. Petr Pelech
I have done my reasearch mainly in the area of the calculus of variations, partial differential equations, and continuum thermodynamics.
In particular, I have been studying rate-independent processes in solids with the focus on inelastic behaviour of materials in a large-strain regime. The works have addressed on one side the proper notion of a weak solution and the question of its existence (stress has been put on variational mathods), on the other thermodynamic consistency of the model under consideration, building mainly on the concept of generalized standard solid.
More recently, I have started to investigate gradient flows in Banach spaces, to larger extend using the minimizing movement scheme, and to study their limiting behaviour for various time scales.
Last but not least, I have been also interested in GENERIC (General Equation for Nom-Equilibrium Reversible-Irreversible Coupling), focusing mainly on modeling of complex, visco-elasto-plastic fluid-solids, and mathematical analysis of static models in Peridynamics, a nonlocal theory of the mechanics of solids.
Publications and Preprints
- Gradient polyconvexity and modeling of shape memory alloys. Preprint., WIAS Preprint No. 2851. .
- On compatibility of the Natural configuration framework with GENERIC: Derivation of anisotropic rate-type models. Preprint., WIAS Preprint No. 2856 arXiv:2010.06903. .
- Separately Global Solutions to Rate-Independent Processes in Large-Strain Inelasticity. Preprint., arXiv:2008.02244. .
- Gradient Polyconvexity in Evolutionary Models of Shape-Memory Alloys. J. Optim. Theory Appl., 184, 2020. 10.1007/s10957-019-01489-9 arXiv:1807.09855. .
- The peridynamic stress tensors and the non-local to local passage. Z Angew Math Mech., 2019. 10.1002/zamm.201800010 arXiv:1711.08445. .
PELECH, Petr. Variational Methods in Thermomechanics of Solids. Praha, 2020. Dizertační práce. Univerzita Karlova, Matematicko-fyzikální fakulta. Vedoucí práce Kružík, Martin. (Charles Univerzity Digital Repository)
|Since Oct 2020||Member of the research group Partial Differential Equations at the Weierstrass Institute.|
|Sep 2020|| Doctoral defense at Charles University, Faculty of Mathematics and Physics.
Advisor: Doc. Martin Kružík;
|Oct 2014 – Sep 2016||Studies M.Sc. Mathematical Modelling at Charles University, Faculty of Mathematics and Physics|
|Oct 2011 – Sep 2014||Studies B.Sc. Mathematics at Charles University, Faculty of Mathematics and Physics|
Last modified: 2021-08-06 by Petr Pelech