Dr. Petr Pelech

Scientific interests
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 rateindependent processes in solids with the focus on inelastic behaviour of materials in a largestrain 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 NomEquilibrium ReversibleIrreversible Coupling), focusing mainly on modeling of complex, viscoelastoplastic fluidsolids, 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. Variational Views in Mechanics., 10.1007/9783030900519_5, WIAS Preprint No. 2851. .
 On compatibility of the Natural configuration framework with GENERIC: Derivation of anisotropic ratetype models. J. NonNew. Fluid Mech., 10.1016/j.jnnfm.2022.104808, WIAS Preprint No. 2856, arXiv:2010.06903. .
 Separately Global Solutions to RateIndependent Processes in LargeStrain Inelasticity. Nonlinear Analysis., 10.1016/j.na.2021.112668, arXiv:2008.02244. .
 Gradient Polyconvexity in Evolutionary Models of ShapeMemory Alloys. J. Optim. Theory Appl., 184, 2020. 10.1007/s10957019014899, arXiv:1807.09855. .
 The peridynamic stress tensors and the nonlocal to local passage. Z. Angew. Math. Mech., 2019. 10.1002/zamm.201800010 arXiv:1711.08445. .
Thesis
PELECH, Petr. Variational Methods in Thermomechanics of Solids. Praha, 2020. Dizertační práce. Univerzita Karlova, Matematickofyzikální fakulta. Vedoucí práce Kružík, Martin. (Charles Univerzity Digital Repository)
Short CV
Jan 2023  Member of the Biomembrane Remodeling Group at the Faculty of Mathematics and Physics, Charles University. 
Oct 2020 – Dec 2022  Member of the research group Partial Differential Equations at the Weierstrass Institute, Forschungsverbund Berlin e.V. 
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: 20231015 by Petr Pelech