7.1.2008
15:40
 Prof. Dr. Christian Rohde (University of Stuttgart): Modelling of Liquid-Vapour Flows: Diffuse Interface versus Sharp Interface and Mesoscopic versus Macroscopic Models
17:20
 Doc. RNDr. Jiri Langer, CSc. (UTF, MFF UK, Prague): Je hospodin hospodarny? (in czech)
 18.2.2008
15:40
 Prof. Jens Frehse (Institut fur Angewandte Mathematik, University of Bonn): Diagonal elliptic and parabolic systems with superquadratic Hamiltonians Abstract: We consider elliptic or parabolic systems (ut ) − ∆u = H (∇u) + f where u is a vector function, periodic in the space variables. Under additional special structure conditions for H (the ?Hamiltonian?) and natural smoothness conditions on the data we prove the existence of regular solutions ? without smallness conditions ? in the case that H ( ∇u) grows like a polynomial in |∇u|. Up to now, in the case of systems of equations, only Hamiltonians growing at most quadratically in |∇u| have been treated. The work has been done in collaboration with Alain Bensoussan (Dallas, USA).
 25.2.2008
15:40
 priv.doz. RNDr. Martin Kruzik, PhD. (UTIA, ASCR, Prague and Dep. of Physics, Civil engineering, CVUT, Prague): Oscillations and concentrations generated by A-free mappings and weak lower semicontinuity of integral functionals Abstract: We use a generalization of Young measures to describe oscillations and concentrations in sequences of maps in $L^p(\O;\R^m)$ satisfying a linear differential constraint ${\mathcal A}u_k=0$. Applications to sequential weak lower semicontinuity of integral functionals along ${\mathcal A}$-free sequences and to weak continuity of determinants are given, too. This is a joint work with I. Fonseca (CMU, Pittsburgh)
17:20
 Prof. Ing. Tomas Roubicek, DrSc. (Mathematical Institute, Charles University, Prague): Rate independent processes in viscous solids Abstract: Abstract: Generalized standard solids with internal parameters describing activated typically rate-independent processes such as plasticity, damage, or phase transformations, ferromagnets or ferroelectrics, will be described as a system of a force-equilibrium equation and variational inequality for internal parametr variable. Various definitions of weak solutions will be examined, especially from the viewpoint of ability to combine rate-independent processes and other rate-dependent phenomena, as viscosity or inertia. The talk will emphasize mathematical aspects (contrary to modelling itself, as already exposed on Nov.12, 2007)
 3.3.2008
15:40
 Prof. Dr. A. Mielke (WIAS & HU Berlin): Analysis of Rate-Independent Materila Models: I. Classical rate-independent models including elastoplasticity Abstract: Some physical processes like dry friction, elastoplasticity, damage, hysteresis in ferromagnets and shape-memory alloys can be modeled by rate-independent material laws. We provide mathematical models for such processes and discuss general existence results based on the energetic formulation which is based on the dissipation distance and the stored-energy funtional. Several applications are given and the uestion of convergence of solutions under Gamma convergence of the unctionals is addressed. The latter theory provides convergence of umerical schemes and homogenization results.
 10.3.2008
15:40
 Prof. Dr. A. Mielke (WIAS & HU Berlin): Analysis of Rate-Independent Materila Models: III. Applications in material models Abstract: Some physical processes like dry friction, elastoplasticity, damage, hysteresis in ferromagnets and shape-memory alloys can be modeled by rate-independent material laws. We provide mathematical models for such processes and discuss general existence results based on the energetic formulation which is based on the dissipation distance and the stored-energy funtional. Several applications are given and the uestion of convergence of solutions under Gamma convergence of the unctionals is addressed. The latter theory provides convergence of umerical schemes and homogenization results.
17:20
 Dr. Chiara Zanini (Dep. of Mathematics and Computer Sciences, University of Udine, Italy and Institute of Physics AS CR, Prague): Mathematical models of quasistatic crack propagation Abstract: We consider the propagation of a single crack along a prescribed crack path and discuss two notions of evolution of brittle fractures inspired by Griffith s theory. The first one corresponds to the energetic solution for rate-independent processes introduced by Mielke, and is based on a global stability criterion. The second one, more recent, uses a different selection criterion and is based on local minimality. We compare these two notions in an explicit example.
 17.3.2008
15:40
 Prof. Dr. P. Exner (Dep of Theoretical Physics, Nuclear Physics Institute, ASCR): Klasicke a kvantove isoperimetricke problemy resene pomoci nerovnosti pro delky tetiv Abstract: Prednaska je motivovana isoperimetrickymi problemy, jez vznikaji v kvantove mechanice i v klasicke fyzice. Budeme se zabyvat Schrodingerovymi operatory v L2(R2) se singularni pritazlivou interakci, jejimz nosicem je uzavrena krivka. Abstract
 31.3.2008
15:40
 Prof. Philippe Laurencot (Universite Paul Sabatier, Toulouse): Large time behavior for diffusive Hamilton-Jacobi equations
17:20
 Doc. RNDr. J. Malek, DSc. (Mathematical Institute, Charles University, Prague): Large data existence result for inhomogeneous incompressible heat-conducting fluids
 14.4.2008
15:40
 Prof. Philippe Laurencot (Universite Paul Sabatier, Toulouse): Large time behavior for diffusive Hamilton-Jacobi equations
16:20
 Ing. Jan Zeman, PhD. (Klokneruv ustav, CVUT, Praha): Homogenization of fibrous composites with phase debonding: Rate-independent formulation and numerical solution using FETI-based approach Abstract: Load-induced debonding at internal interfaces is considered to be the dominant damage phenomenon in fibrous reinforced composites, reducing the overall material properties and reduced structural integrity. In the present lecture, a rate-independent multi-scale model of debonding processes is presented, following the ideas introduced recently by Mielke, Roubicek and co-workers. It is shown that the rate-independent setting not only offers a convenient framework for studying the qualitative properties of the solution, but also naturally leads to efficient discretization schemes. As a particular example, we examine a numerical algorithm based on the Finite Element Tearing and Interconnecting (FETI) method. The performance of the algorithm is illustrated on selected numerical examples.
 21.4.2008
15:40
 Dr.Giuseppe Tomassetti (Uni. Rome II Tor Vergata): Coupling dynamic micromagnetics with the heat equation Abstract: In standard micromagnetics the specific magnetization is subject to the saturation constraint, which reflects the assumption that the temperature is well below the Curie point. There exist, however, interesting evolution processes, some of them of technological importance, where temperature instantaneously rises above the Curie point in a very small portion of the body. Modeling these processes requires a suitable nonisothermal extension of micromagnetics. In this talk, which is based on an ongoing collaboration with Paolo Podio-Guidugli and Tomas Roubicek, it will illustrated how to produce such an extension using standard tools from continuum thermomechanics. Both modeling and analytical issues will be discussed.
 28.4.2008
15:40
 Dr Jonathan J. Healey (School of Computing and Mathematics, Keele University, UK): Instabilities of mixing layers
17:20
 Dr. Lucia Scardia (MPI MIS Leipzig): Damage as Gamma-limit of microfractures in linearized elasticity Abstract: A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. In particular, damage is obtained as limit of periodically distributed microfractures.
 5.5.2008
15:40
 Prof. Dr. E. Miersemann (Mathematisches Institut, Universitat Leipzig, Germany): On liquid layers in cavities
 12.5.2008
15:40
 Dr. M. Bulicek (Mathematical Institut, Charles University, Prague): On the existence of an entropy solution to scalar hyperbolic conservation laws with discontinuous flux Abstract: We will present an observation how the theory on existence of soution to scalar hyperbolic conservation laws can be extended to the case when the flux function has a finite number of monotone jumps. We will also introduce a natural notation for entropy and measure-valued entropy solution for such fluxes.
 19.5.2008
15:40
 Mgr. Josef Kristan (NCMM, Prague): Modelling of elementary processes of plastic deformation of crystalline materials
 26.5.2008
15:40
 Dr. M. Lund (Institute of Organic Chemistry and Biochemistry, ASCR): Coarse-Grained Models for Molecular Systems
16:20
 Prof. Ing. Frantisek Marsik, DrSc. (Institute of Thermodynamics, ASCR): Modeling of biochemistry of bone reconstruction
16:40
 Prof. Ing. Tomas Roubicek, DrSc. (Mathematical Institute, Charles University): Incompressible ionized non-Newtonean fluid mixtures
17:00
 Doc. RNDr. Josef Malek, CSc. (Mathematical Institute, Charles University): Incompressible chemically-reacting fluids
 6.10.2008
15:40
 Prof. Dr. Gert Lube (Institut fuer Numerische und Angewandte Mathematik (NAM), Georg-August-Universitat Gottingen, Germany): Stabilized finite element methods for thermally coupled incompressible flows Abstract: The talk is concerned with stabilized finite element methods for the incompressible Navier-Stokes problem with thermal coupling. Turbulent flows are simulated based on an unsteady Reynolds-averaged Navier-Stokes (URANS) model. In the discrete case, an equal-order interpolation is applied to all unknowns. Some aspects of classical residual-based stabilization techniques like streamline-upwind stabilization (SUPG), pressure stabilization (PSPG), stabilization of the divergence-free constraint (div-div stabilization) and the treatment of boundary and interior layers will be addressed. Finally, some applications to indoor-air flow simulation are given.
17:20
 Prof. Hans Christian Oettinger (ETH Zurich, Department of Materials, Institute of Polymers, Zurich, Switzerland): Mathematical Structure of Thermodynamics and Its Preservation in Coarse Graining Abstract: Coarse graining is NOT a necessary evil required to solve problems which are computationally too large. Coarse graining rather is the art to simplify to the essentials and hence to provide understanding. Systematic coarse graining procedures are therefore needed, which are the topic of statistical equilibrium and nonequilibrium thermodynamics. We show that any coarse graining step should be accompanied by an increase in irreversibility and is potentially accompanied by the same kind of historical confusion that was created by the passage from reversible to irreversible equations. The relevant thermodynamic structure and the coarse graining recipes suggested by statistical mechanics are described in detail and are illustrated by the example of hydrodynamics. We employ systematic coarse graining techniques to derive hydrodynamic equations from Grad s ten-moment equations. The coarse graining procedure is designed such that it manifestly preserves the thermodynamic structure of the equations. A number of mathematical challenges associated with structure-preserving coarse graining of evolution equations for thermodynamic systems as a generalization of Hamiltonian dynamic systems and reduction techniques are presented. Coarse graining is a key step that should always be considered before attempting to solve an equation.
 13.10.2008
15:40
 Prof. Dr. Maria Lukacova (Institute of Numerical Simulation, Hamburg University of Technology, Germany): Finite volume evolution Galerkin method : theory and application for geophysical flow
17:20
 Prof. Dr. Gert Lube (Institut fuer Numerische und Angewandte Mathematik (NAM), Georg-August-Universitat Gottingen, Germany): Local projection stabilization methods for singularly elliptic problems Abstract: The concept of variational multiscale methods (VMS) is the starting point of the talk. The first goal is to describe the link of local projection stabilization (LPS) techniques to the VMS framework. Then we present recent results on the a-priori analysis for LPS methods applied to the basic linear advection-diffusion-reaction problem. Moreover, a critical comparison to the standard streamline-diffusion stabilization will be given.
 20.10.2008
15:40
 Prof. Dr. Gert Lube (Institut fuer Numerische und Angewandte Mathematik (NAM), Georg-August-Universitat Gottingen, Germany): Calibration of subgrid viscosity models for turbulent incompressible flows Abstract: We start with some requirements for the large eddy simulation (LES) of incompressible flows. Then we consider the variational multiscale approach to LES and discuss a parameter identification problem for the corresponding subgrid-scale model. Finally, we present some recent results for the LES with a collocated finite volume code applied to standard benchmark problems and give some conclusions for the finite element case.
 27.10.2008
15:40
 Seminar canceled
 3.11.2008
15:40
 Dr. Johannes Zimmer (Dep. of Mathematical Sciences, University of Bath, UK): From conservative lattice models for elasticity to macroscopic dissipation Abstract: We consider travelling waves in a one-dimensional chain of atoms with nearest neighbour interaction. The elastic potential is piecewise quadratic and the model is thus capable of describing phase transitions. We show that for suitable fixed subsonic waves, there is a family of heteroclinic travelling waves (connecting both wells of the energy). Though the microscopic picture is Hamiltonian, we derive non-trivial so-called kinetic relations on the continuum scale; they can be related to the dissipation generated by a moving phase boundary. It turns out that the microscopic asymmety determines here the macroscopic dissipation. This is joint work with Hartmut Schwetlick (Bath).
17:20
 Prof. Roger Lewandowski (University Rennes 1, France): Simple results for 3D NSE in periodic case Abstract: Part I - Some remarks on Sobolev spaces for periodic functions
 10.11.2008
15:40
 Dipl.-Math. Marita Thomas (Humboldt Universitat zu Berlin): Existence analysis of rate-independent damage processes Abstract: We analyze a model describing partial damage of a solid within its energetic formulation. This approach involves the free energy functional of the body and the dissipation potential expressing the evolution of damage. We provide an existence result in the small strain as well as in the finite strain setting and give examples on energy densities covered by our theory.
17:20
 Prof. Roger Lewandowski (University Rennes 1, France): Simple results for 3D NSE in periodic case Abstract: Part III - Deconvolution models, still in the periodic case
 17.11.2008
15:40
 seminar canceled
 24.11.2008
15:40
 Prof. RNDr. Jiri Mls, CSc. (Prirodovedecka fakulta UK): Pretvareni nasycenych porovitych teles Abstract: 1. nasycene porosni prostredi jako dvoufazovy system, 2. rozlisovaci uroven, 3. Darcyuv zakon, 4. pretvareni, 5. Biotova teorie.
17:20
 Dr. Sebastian Franz (TU Dresden): Superconvergence for singularly perturbed problems with parabolic layers
 1.12.2008
14:00
 Prof. Dr. Barbara Wohlmuth (University of Stuttgart, Germany): Stabilized semi-smooth Newton algorithms for variational inequalities Abstract: Numerical simulation for partial differential equations plays an important role in many fields. Although efficient solution strategies are well known for simple settings, more complex models involving non-smooth nonlinearities are still quite challenging. In this talk we present some applications from structural mechanics and finance where variational inequalities play an important role. Surprisingly frictional contact problems with plasticity fit into the same mathematical framework as American options. We propose fast and robust numerical approaches based on the concept of domain decomposition, adaptivity and stabilized time integration.
15:40
 Prof. Dr. Christof Eck (University of Bielefeld, Germany): Existence results for contact problems with friction Abstract: Contact problems in elasticity belong to the classical topics of applied mathematics, but there are still many questions unsolved, in particular if friction is taken into account. The main difficulty is the combination of the unilateral contact condition with the Coulomb friction law that leads to a non-monotone and non-compact formulation. This requires special approaches to prove the existence of solutions. The most successful approach to analyze contact problems with Coulomb friction was established by Jindrich Necas together with Jiri Jarusek and Jaroslav Haslinger in a seminal paper On the solution of the variational inequality to the Signorini problem with small friction. (Boll. Un. Mat. Ital. B 5(17), pp. 943-958). It consists in the approximation of the problem by some convex problem, the proof of some addition regularity of the solution by a certain translation technique and the application of a fixed point argument. This approach was first applied to static contact problems with Coulomb friction. It was later extended to many other types of frictional contact problems, as e.g. quasistatic contact problems and dynamic problems for viscoelastic and viscoplastic materials. Some results also include the transport of heat generated by friction. In the lecture we present this approach and give a survey on the available existence results for static, quasistatic and dynamic frictional contact problems.
16:50
 Prof. RNDr. Igor Bock, Ph.D. (Slovak University of Technology Bratislava, Slovakia): Dynamic Contact Problems for von Karman Plates Abstract: We deal with systems consisting of a nonlinear hyperbolic variational inequality for a deflection and a nonlinear elliptic equation for the Airy stress function. The systems describe moderately large deflections of thin elastic and viscoelastic plates with an inner obstacle and in a dynamic action. The dynamic contact problems are not frequently solved in the framework of variational inequalities. Mainly for the elastic problems there is only limited amount of results available. The aim of the presentation is to extend these results to von K arm an plates. We neglect the rotational inertia member in the elastic case. We will consider the short memory and the long memory material in the case of a viscoelastic plate. The fist one is expressed by a pseudo-hyperbolic unilateral problem. The long memory material will be considered as an integro-differential variational inequality with a singular kernel.
 8.12.2008
15:40
 Prof. Martin Hairer (University of Warwick, UK): Ergodic Theory for Stochastic PDEs I. Abstract: The aim of these lectures is to present a reasonably self-contained theory of ergodicity for stochastic processes that is sufficiently flexible to allow to deal with infinite-dimensional problems like the stochastic Navier- Stokes equations, stochastic reaction-diffusion equations, etc. In the first lecture, we will introduce the main objects and problems, and remind the audience of the classical theory of Harris chains. We will go through elementary sketches of proofs of some of the main results of this theory. In the second lecture, we will argue that the theory of Harris chains is not suitable for infinite-dimensional problems and we will lay down the foundations for a modified theory that is more flexible. The remainder of the course will be devoted to the applications of this theory to a class of stochastic PDEs. In the third lecture, we will sketch the proof of a general ergodicity result. The final lecture will be devoted to showing how to leverage the bounds obtained in the third lecture to obtain an exponential convergence result.
17:20
 Prof. Martin Hairer (University of Warwick, UK): Ergodic Theory for Stochastic PDEs II.
 15.12.2008
15:40
 Doc. RNDr. Lubos Pick, CSc., DSc. (Charles University, Prague): Sobolev Spaces and their Optimality in Embeddings - Old and New Abstract: We develop a new method that enables one to test whether a given Sobolev embedding can or cannot be improved in the framework of the rearrangement-invariant spaces. The method is applicable to various tasks including Sobolev embeddings, boundary trace embeddings, logarithmic Sobolev inequalities etc.
17:00
 Doc. RNDr. Lubos Pick, CSc., DSc. (Charles University, Prague): The Gateway to Compactness Abstract: We focus on finding the frontier (if only such a thing exists) between boundedness and compactness of a Sobolev embedding. We apply the result to obtaining a manageable condition equivalent to saying that a Sobolev embedding involving a pair of rearrangement - invariant spaces is compact.

 Po semináři se podává opět čaj a káva. Všichni zájemci jsou srdečně zváni.