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Grants





Mathematical analysis of complex systems in the fluid mechanics (201/08/0315)
from 01/01/2008
to 31/12/2011 investigator

The main goal of the project is to develop a rigorous mathematical theory of complex systems in fluid mechanics. Such problems arise in models of chemical reactions, astrophysics, biological models, atmosphere and geophysical fluid dynamics. The main challenge here is to handle problems with large data and without any restriction concerning the time scale. The main topics include: Multicomponent problems and mixtures. 2. Equations of magnetohydrodynamics. 3. Atmospheric and geophysical models. 4. Large time behavior of solutions and equilibrium states.



Nečas Center for Mathematical Modeling  part IM (LC06052)
from 01/01/2006
to 31/12/2011 investigator

The general goal of the Nečas Center for Mathematical Modeling is to establish a significant scientific team in the field of mathematical properties of models in continuum mechanics and thermodynamics, developed by an intensive collaboration of five important research teams at three Prague affiliations and their goaldirected collaboration with top experts from abroad. The research projects of the center include: 1) Nonlinear theoretical, numerical and computer analysis of problems of continuum physics. 2) Heatconductive and deforming processes in compressible fluids, incompressible substances of fluid type, and in linearly elastic matters. 3) Interaction of the substances. 4) Biochemical procedures in substances. 5) Passages between models, dimensional analysis.



Asymptotic analysis of infinite dimensional dynamical systems (IAA100190606)
from 01/01/2006
to 31/12/2008 investigator

The goal of the project is to obtain new qualitative results concerning the asymptotic behavior of infinite dimensional dynamical systems arising especially in the theory of viscous compressible fluids. The main topics include compactness of solutions, global existence, convergence towards equilibria and problems with rapidly oscillating boundaries.



Mathematical analysis in the thermodynamics of fluids (201/05/0164)
from 01/01/2005
to 30/12/2007 investigator

The aim of the present research project is to establish a coherent mathematical theory of viscous heat conducting fluids based on a suitable variational formulation of the problem consistent with the second law of thermodynamics. The main topics include: 1. The existence of solutions on arbitrarily large time intervals with no restriction on the size of data. 2. The questions of uniqueness, boundedness, and stability of solutions with respect to the initial conditions and other parameters as the case may be. 3. The long time behavior, convergence towards equilibria, and attractors. 4. Sensitivity analysis with respect to the shape of the underlying spatial domain.



Compatibility of dynamics and statics in multicomponent dissipative systems (IAA1019302)
from 01/01/2003
to 01/01/2005 investigator

The main topics of the project is to study the asymptotic behaviour of solutions to partial differential equations arising in multicomponent systems modelling. The long time behaviour of solutions as well as the problem of stabilization towards stationary state will be investigated. Specifically, we shall investigate: 1. The equations describing the motion of one or several rigid bodies in a viscous fluid. 2. The solidliquid phase fields models. 3. Dynamical solidsolid phase transition models.
