International Cooperation


Grant: 1906175J
from 01/01/2019
to 31/12/2021
Grantor: Czech Science Foundation

Compositional Methods for the Control of Concurrent Timed DiscreteEvent Systems


Objectives:
Current approaches for control of timed discreteevent systems (DES) with dense real time only deal with monolithic plants, which means that their control suffers from high complexity and even decidability issues (non existence of finite state controllers). In order to face these issues, it is important to develop computationally efficient compositional approaches, such as modular control. We will investigate modular and coordination control of timed DES modeled by timed Petri nets or by (max,+)automata.



Grant: 7AMB16PL060
from 01/01/2017
to 31/12/2018
Grantor: Ministry of Education, Youth and Sports  MŠMT

Flow of viscous fluid in time dependent domain


Objectives:
G1. Global existence of weak solution of full system in timedependent domain.
Goals: Our goals is the study of the global existence of a weak solution in the case of a bounded or an exterior domains for the Navier or Dirichlet type of boundary conditions. We will use the method introduced in E. Feireisl: Dynamics of viscous compressible fluids, 2004 for fixed domain and we will also apply the penalization method.
G2: Relative entropy inequality.
Goals: We will focus on the derivation of the relative entropy inequality in the case of timedependent domain. We will use the results from fixed domain introduced in E. Feireisl and A. Novotný: Weakstrong uniqueness for the full NavierStokesFourier system, 2012.
G3. Singular limits.
Goals We shall study the singular limits in the regime of low Mach number. From this follows that the limit system (target system) is the system of incompressible flow in the timedependent domain. We will use the results from E. Feireisl, O. Kreml, Š. Nečasová, J. Neustupa, J. Stebel: Incompressible limits of fluids excited by moving boundaries, 2014, where barotropic case was studied, and also the results for fixed domains.
G4: Weak solution of viscous flow around rotating rigid body and his asymptotic behavior.
Goals: We will focus on the problem of existence of weak solution in weighted Lorentz spaces to get the asymptotic behavior of flow around a body. Because of the lack of the regularity in L^{p} spaces it is necessary to go into more complicated structure of Lorentz spaces, where the integrability of convective term is satisfied. Moreover, we would like to study the relative entropy inequality in the case of compressible flow around rotating body.



Grant: GF1733849L
from 01/01/2017
to 31/12/2019
Grantor: Austrian Science Foundation (FWF)  Czech Science Foudation

Filters, Ultrafilters and Connections with Forcing


Objectives:
The project falls within the scope of Set Theory & Foundations of Mathematics, specifically Combinatorial Set Theory and Forcing. We will investigate new combinatorial and forcing methods for constructing ultrafilters with special properties in different models of Set Theory.It will use these methods to answer independence questions about ultrafilters (no Ppoints with a large continuum or small character filters), structural questions about filters (which ultrafilters/filters contain towers) and questions about the related cardinal invariants (independence number, free sequence number). It is known that current methods cannot answer some of these questions so the project will have to come up with novel ideas. The methods used will include forcing iterations, diamondlike constructions, preservation theorems and methods from descriptive set theory.



Grant: 7AMB17FR053
from 01/01/2017
to 31/12/2018
Grantor: Ministry of Education, Youth and Sports  MŠMT

Dynamics of mutlicomponent fluids


The goal of the project is studying qualitative properties of a particular class of the socalled energetically weak solutions to complex system of the NavierStokesFourier type as well as Coupling of these systems with the phase transition equations of the CahnHilliard or AllenCahn type. We plan to investigate these problems also in unbounded physical domains in appropriate classes of uniformly bounded functions.
The main goal is obtaining new results in the following directions:
• applications of the relative entropy methods and the consequences concerning stability of the socalled dissipative solutions
• singular limits, in particular the sharp interface limits with rigorous mathematical justification
• longtime dynamics, with a particular emphasis on the existence of bounded absorbing sets, asymptotic compactness of greajectories and the relevant questions concerning the attractors and their structure and complexity
