International Cooperation
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Grant: GC19-06175J
from 01/01/2019
to 31/12/2021
Grantor: Czech Science Foundation
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Compositional Methods for the Control of Concurrent Timed Discrete-Event Systems
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Objectives:
Current approaches for control of timed discrete-event 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.
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Grant: 7AMB16PL060
from 01/01/2017
to 31/12/2018
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Flow of viscous fluid in time dependent domain
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Objectives:
G1. Global existence of weak solution of full system in time-dependent 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 time-dependent domain. We will use the results from fixed domain introduced in E. Feireisl and A. Novotný: Weak-strong uniqueness for the full Navier-Stokes-Fourier 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 time-dependent 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 Lp 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.
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Grant: GF17-33849L
from 01/01/2017
to 31/12/2019
Grantor: Austrian Science Foundation (FWF) - Czech Science Foudation
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Filters, Ultrafilters and Connections with Forcing
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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 P-points 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, diamond-like constructions, preservation theorems and methods from descriptive set theory.
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Grant: 7AMB17FR053
from 01/01/2017
to 31/12/2018
Grantor: Ministry of Education, Youth and Sports - MŠMT
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Dynamics of mutli-component fluids
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The goal of the project is studying qualitative properties of a particular class of the so-called energetically weak solutions to complex system of the Navier-Stokes-Fourier type as well as Coupling of these systems with the phase transition equations of the Cahn-Hilliard or Allen-Cahn 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 so-called dissipative solutions
• singular limits, in particular the sharp interface limits with rigorous mathematical justification
• long-time 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
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