8.1.2007
15:45
 RNDr. Eduard Feireisl, DrSc. (Mathematical Institute AS CR, Prague): Fluid dynamics problems on domains with rapidly oscillating boundaries: Is it always optimal when Young measures reduce to Dirac masses?
 19.2.2007
15:40
 Prof. A. Novotny (Universite du Sud Toulon-Var (France)): Low Mach number limits to the complete Navier-Stokes-Fourier system
 26.2.2007
15:40
 Prof. Dr. Anna-Margaret Saendig (IANS, Univeritaet Stuttgart, Germany): Variational methods for nonlinear boundary value problems in elasticity
17:20
 Prof. Antonín Novotný (Universite du Sud Toulon-Var, France): Low Mach number limits to the complete Navier-Stokes-Fourier system
 5.3.2007
15:40
 Prof. Dr. Ch. Grossmann (TU Dresden, Germany): Domain decomposition methods
17:20
 Prof. Dr. R. Farwig (TU Darmstadt, Germany): From the Theory of Very Weak Solutions to Regularity of Weak Solutions of the Instationary Navier-Stokes System Abstract: The three lectures deal with the theory of very weak solutions to the stationary and instationary Stokes and Navier-Stokes equations. Very weak solutions define a new class of solutions with no differentiability and not necessarily finite energy, but with uniqueness properties. The aim of this series of lectures is to apply this theory to questions of regularity of weak solutions of the Navier-Stokes equations in the sense of Leray-Hopf and to prove local or even global in time regularity beyond Serrin s condition.
 12.3.2007
15:40
 Doc. RNDr. L. Pick, DrSc. (KMA MFF UK): Optimal Sobolev Embeddings and Interpolation
17:20
 Dr. J. Schneider (NCMM, Prague): Function Spaces of Varying Smoothness
 19.3.2007
15:40
 Dr. C. Schwarz (TU Muenchen, Germany): Continuum dislocation-based plasticity: numerical implementation and short-range interactions Abstract: In this talk, the latest advances on the continuum dislocation-based model of plastic deformation will be presented, both concerning the numerical implementation and the modelling. In this deterministic model, the description of evolving fields of curved dislocations is embedded in the rigorous framework of small strain continuum mechanics. The model explains the size-dependent plastic response of crystalline materials at the scale of micrometers.
17:20
 Dr. D. Wachsmuth (Institute of Mathematics, TU Berlin, Germany): Optimal control of the unsteady Navier-Stokes equations Abstract: The talk is concerned with the study of optimal distributed control problems for the non-stationary Navier-Stokes equations. The control $u$ in our problem is vector-valued. Thus, box-constraints are not the only possible choice of a control constraint. Therefore, we consider pointwise convex control constraints of the form $u(x)in U(x)$, where $U$ is an set-valued mapping with convex and closed images. We present necessary as well as sufficient optimality conditions for that general type of constraint. The first-order necessary conditions imply a representation of locally optimal controls by projections, a fact which leads to new regularity results. In the presence of box-constraints and under the assumption of sufficient optimality conditions, locally optimal controls are stable with respect to small perturbations. This stability result directly gives the local quadratic convergence of the SQP-method for our optimal control problem. The talk closes with an outlook on open questions, which are connected to regularity issues of the Navier-Stokes system.
 26.3.2007
15:40
 Prof. Dr. Dietmar Kröner (Dep. of Applied Mathematics of University Freiburg, Freiburg, Germany): Phase transitions for liquid vapor flows Abstract: Vapor together with liquid phases occur in many applications like cavitation problems, two phase flows in micro devices, cooling and boiling processes and breakup of liquid jets. Since e.g. turbine blades and ship propellers can be destroyed by cavitation this research is of high industrial interest. Both phases are transported by the flow and undergo phase transitions. The governing mathematical equations are expressed by the basic conservation laws for mass, momentum (, and energy) together with suitable equations of state for all phases. Additionally, for the mass transfer across the phase boundaries special treatment is necessary. A very important issue is the simultaneous treatment of phase transition and compressible flow. Up to now the dynamics of pure phase transition (free boundary value problems, Stefan problems, Cahn-Hilliard problem, Landau-Ginzburg equation etc.) as well as the dynamics of compressible (viscous) flow have been studies very extensively but separately. The most basic experiment on liquid vapor flows considers the dynamics of a single vapor bubble in a container filled with liquid. If the outer pressure of the liquid is decreased to vapor pressure then the liquid vapor interface starts to move: We have a dynamic phase boundary with mass transfer. In more complex settings this occurs during the process of cavitation. Lord Rayleigh discovered that pressure waves emitted during the process of cavitation near rigid walls may damage the walls. This can be observed on the surface of ship propellers. Mathematical models for liquid vapor phase transitions can be divided into two classes: diffuse interface and sharpe interface models. The first class takes into account the internal structure of a phase boundary and resolves it as a steep but continuous transition. In the second class phase boundaries are discontinuous transitions of the thermodynamical variables. We will consider the mathematical model which is given by the compressible Navier-Stokes-Korteweg equations which consists of the classical Navier_Stokes equations and additional higher order derivatives of the density on the right-hand side of the momentum equations, multiplied by a small parameter $lambda$. In this lectures we will present an overview of theoretical results concerning existence, the interface conditions for the pressure in the limit if $lambda$ tends to zero and about some numerical experiments.
 2.4.2007
15:40
 MUDr. Vladimir Prochoda (FTN Krc): Modelovani kancerogeneze bunky kolorektalniho karcinomu Abstract: Strucny popis geneze kolorektalniho karcinomu - vyvoj, stadia a casova osa. Charakterizace 3 modelu pro popis chovani kancerogeneze kolorektalniho karcinomu v ruznych stadiiich ( 1/ kancerogeneze bunky kolorektalniho karcinomu 2/ vyvoj kolorektalniho karcinomu do urovne karcinoma in sinu 3/ distribucni model pro distribuci ndoru do kompartmentu) - vztah a prolinani techto stadii. Pozornost bude venovana predevsim na exploataci moznosti matematickeho nebo jinak abstrahovaneho modelovani s naslednou aplikaci do tvaru enginu, ktery by bylo mozno virtualne zpracovavat na PC. Hlavn podminkou je vytvorit ciselne rady pro nezavisle promenne /ovlivnujici faktory geneze/ a zavisle promenne /ukazatele geneze/. Problematika se bude tykat i vytvoreni formulaci pro zpetne vazby procesu.
 9.4.2007
Seminář se nekoná - Velikonoce
 16.4.2007
15:40
 Prof P. Podio-Guidugli (Dipartimento di Ingegneria Civile, Universita di Roma, Italy): Remarks on the notion of aggregation state for complex materials Abstract: In standard continuum mechanics, a material body is termed simple' if its mechanical response depends only on the history of its deformation gradient. As to their aggregation state, simple materials are sorted into solids and fluids according to a well-known algebraic criterion proposed by W.Noll. There is no such criterion for complex' (i.e., not simple) materials. In this talk, I shall try and propose one, based on certain specifications of the internal working.
 23.4.2007
15:40
 Dr. A. Timofte (Institute of Mathematics, Romanian Academy, Bucharest): Two-scale homogenization for evolutionary variational inequalities Abstract: This topic (subject of a joint work with Alexander Mielke) is devoted to the two-scale homogenization for a class of rate-independent systems described by the energetic formulation or equivalently by an evolutionary variational inequality. In particular, we treat the classical model of linearized elastoplasticity with hardening. The associated nonlinear partial differential inclusion has periodically oscillating coefficients, and the aim is to find a limit problem for the case that the period tends to 0.
17:20
 Dr. Jonathan Healey (Department of Mathematics, Keele University, Keele, United Kingdom): Destabilizing fluid flows by confinement
 30.4.2007
Seminář se nekoná
15:40
 No program for this date.
 7.5.2007
15:40
 prof. Dr. P. J. Rabier (Dep. of Mathematics, University od Pittsburgh, USA): Degree theory for nonlinear Fredholm mappings of index 0 (lecture 1 of 5) Abstract: This mini-course will discuss the Fredholm and related properties of partial differential operators on unbounded domains and their applications to linear and nonlinear PDEs. The course is divided in 5 lectures, briefly described below. Since most technical details will not be addressed during the lectures due to time limitation, a list of relevant references dealing with such details will be provided with each lecture. 7.5. Lecture 1: "Degree theory for nonlinear Fredholm mappings of index 0" 9.5. Lecture 2: "Fredholm and properness properties of elliptic operators on R^N" 28.5. Lecture 3: "Nonlinear problems with infinitely many solutions" 29.5. Lecture 4: "Decay transference and applications" 30.5. Lecture 5: "The index of evolution operators"
17:20
 Prof. Jan Sokolowski (Laboratoire de Mathmatiques, Universite Henri Poincare Nancy I, France): Shape optimization for spectral problems - singular boundary perturbations Abstract: In a joint research with S.A. Nazarov we perform the asymptotic analysis of eigenvalues and eigenfunctions of elliptic spectral problems with respect to singular perturbations of small size, in the form of cowerns, boundary cracks and knops. The asymptotics are justified by the method of compound asymptotic expensions.
 14.5.2007
15:40
 no program for this date
 21.5.2007
15:40
 Prof. Dr. Torsten Linss (TU Dresden, Germany): Parameter robust methods for systems of singularly perturbed problems
17:20
 Dr. Soeren Bartels (Humboldt-Universitaet zu Berlin, Germany): Aspects in the Modelling, Analysis, and Simulation of Thermoviscoplasticity at Small Strains Abstract: Materials that undergo plastic deformations dissipate mechanical energy into heat. Then, possible changes in temperature influence, in turn, the yield stress which determines the threshold for plastic slip behaviour. In this talk, a simple mathematical model at small strains is proposed and theoretical aspects in the proof of existence of weak solutions are discussed. In particular, sophisticated estimates for the temperature variable are required in order to pass to the limit of Galerkin approximations. Implementation issues such as necessity of numerical integration, usage of weakly acute triangulations, and treatment of a non-smooth potential are adressed. Preliminary illustrative numerical experiments will be shown. This is joint work with Tomas Roubicek.
 28.5.2007
16:15
 prof. Dr. P. J. Rabier (Dep. of Mathematics, University od Pittsburgh, USA): Nonlinear problems with infinitely many solutions (lecture 3 of 5) Abstract: This mini-course will discuss the Fredholm and related properties of partial differential operators on unbounded domains and their applications to linear and nonlinear PDEs. The course is divided in 5 lectures, briefly described below. Since most technical details will not be addressed during the lectures due to time limitation, a list of relevant references dealing with such details will be provided with each lecture. 7.5. Lecture 1: "Degree theory for nonlinear Fredholm mappings of index 0" 9.5. Lecture 2: "Fredholm and properness properties of elliptic operators on R^N" 28.5. Lecture 3: "Nonlinear problems with infinitely many solutions" 29.5. Lecture 4: "Decay transference and applications" 30.5. Lecture 5: "The index of evolution operators"
 18.6.2007
15:40
 Lecture room K1 Doc. RNDr. Josef Malek, CSc. (Mathematical Institut, Charles University, Prague): Blood as an example of non-Newtonean material Abstract: The aim of this talk is to recall basic facts concerning non-Newtonean fluid mechanics, and to illustrate why the blood when considered as a single continuum can be modeled as a viscoelastic shear thinning incompressible fluid.
16:45
 Dr. Frederic Weller (IWR, Universitaet Heidelberg, Germany): Thrombosis & Hemostasis (I): Biology & kinetic considerations Abstract: Hemostasis is responsible to stem blood loss after injury by platelet plug formation. Although being life essential, a major part of deaths in the western society is due to thrombotic events provoked by disorders of the hemostatic system. Therefore, a better understanding of the underlying mechanisms is needed. The first talk presents the biological background and focuses on the kinetics (without taking flow into account). The mechanisms of platelet adhesion/aggregation and the chemical processes are explained in quite detail, the latter both from a cascade and from a cell-based view. Then, the ODE-model of Kenneth Mann serves to study feedback mechanisms, threshold behavior and impairement of thrombin production in the bleeding disorder hemophilia. These findings help to understand hemostatic tests.
17:50
 MUDr. Radek Chabiniok (IKEM, Prague): Thrombosis: A radiological point of view Abstract: The objective of the talk is to show a few practical examples of radiological techniques used in diagnostics of diseases affecting blood vessels and complications of these diseases. Images such as pulmonary embolism acquired by computerized tomography, artery stenoses observed during angiographicexaminations, the nonviable fibrous scar after the myocardial infarction acquired by magnetic resonance imaging will be presented.
 7.9.2007
10:00
Prof. K.R. Rajagopal
(Texas A&M University, College Station, USA):
Thermodynamics of Materials Undergoing Dissipative Processes
Abstract:

## different date and place: this FRIDAY

at UI AV CR, Pod Vodarenskou vezi 2, Praha 8, room c. 318 metro C; tram 10,17,24; bus 103,145,156,177,186,187 - Ladvi, see. SEMINAR Oddeleni vypocetnich metod
 8.10.2007
15:30
RNDr. Eduard Feireisl, DrSc.
(Mathematical Institute, AS CR):
Mathematical theory of multicomponent reactive flows
Abstract: Part of workshop Analysis of Multiphase Problems

### place: UTIA, CAS, Pod Vodrenskou vezi 4, Praha

17:00
Doc. RNDr. Martin Kruzik, PhD.
(Institute of Information Theory and Automation, AS CR):
Gamma-convergence methods and applications
Abstract: Part of workshop Analysis of Multiphase Problems

### place: UTIA, CAS, Pod Vodrenskou vezi 4, Praha

18:15
Prof. Alexander G.Ramm
(Department of Mathematics, Kansas State University, USA):
Creating materials with desired refraction coefficient
Abstract: A method is given for calculation of a distribution of small impedance particles, which should be embedded in a bounded domain, filled with material with known refraction coefficient, in order that the resulting new material would have a desired refraction coefficient. The new material may have some desired wave-focusing properies. For example, it can scatter plane wave mostly in a fixed solid angle. The inverse scattering problem with scattering data given at a fixed wave number and at a fixed incident direction is formulated and solved.

Part of workshop Analysis of Multiphase Problems

### place: UTIA, CAS, Pod Vodrenskou vezi 4, Praha

 15.10.2007
15:40
 Prof. Matthieu Hillairet (Laboratoire MIP, Universite Paul Sabatier, Toulouse): Problem of collision between solid bodies in a viscous fluid Abstract: In the last decade, several studies in fluid-structure interactions showed that collisions between solid bodies in a fluid raise numerous difficulties in the mathematical treatment of such models. In my talk, I shall detail these difficulties and recent results when considering an incompressible fluid.
17:15
 Prof. em. H. Amann, Dr. Dr. h. c. (Institut fur Mathematik, Universitat Zurich): Maximal regularity for parabolic systems in weak settings (lecture no. 3)
 22.10.2007
15:40
 Prof. Bodo Werner (Fachbereich Mathematik, Uni Hamburg, Germany): Microscopic Car Following Traffic models - Road works and macroscopic observations Abstract: here
17:15
 Prof. em. H. Amann, Dr. Dr. h. c. (Institut fur Mathematik, Universitat Zurich): Maximal regularity for parabolic systems in weak settings (lecture no. 5)
 29.10.2007
15:40
 Prof. Joachim Naumann (Humboldt Universitat, Berlin): On the Existence of Weak Solutions to the Equations of Stationary Motion of Perfectly Plastic Fluids Abstract: abstract (pdf)
 5.11.2007
15:40
 Prof. em. Dr.-Ing. Dr. h.c. Wolfgang L. Wendland (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart): Boundary Integral Equations and Pseudodifferential Operators (lecture 1 of 6)
17:20
 Prof. em. Dr.-Ing. Dr. h.c. Wolfgang L. Wendland (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart): Boundary Integral Equations and Pseudodifferential Operators (lecture 2 of 6)
 12.11.2007
15:40
 Prof. Ing. Tomas Roubicek, DrSc. (Mathematical Institute, Charles University, Prague): Rate independent processes in viscous solids and their thermodynamics Abstract: So-called generalized standard solids (of Halphen-Nguen type) involving also activated typically rate-independent processes such as plasticity, damage, or phase transformations, 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. If those rate-dependent phenomena are suppressed, then the system becomes fully rate-independent and then the concept of the so-called energetic solution fully applies. In general case, compromises are needed in definitions, in data qualification, and in results, too. Eventually, thermodynamically consistent coupling with temperature and (inevitably rate-dependent) heat transfer will be scrutinized, too.
 19.11.2007
15:40
 Ing. Miroslav Sedlacek, CSc. (Stavebni fakulta, CVUT): Zakladni parametry odvalovaciho principu Abstract: This lecture will be presented in Czech language.
17:20
 Prof. em. Dr.-Ing. Dr. h.c. Wolfgang L. Wendland (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart): Boundary Integral Equations and Pseudodifferential Operators (lecture 5 of 6)
 26.11.2007
15:40
 Doc. RNDr. Josef Malek, CSc. DSc. (Mathematical Institute of Charles University, Prague): On unsteady flows of Fluids with Pressure, Shear-rate and Temperature Dependent Material Moduli, that slip at solid boundaries Abstract: We rigorously investigate the mathematical properties of unsteady three-dimensional internal flows of incompressible fluids with pressure, shear-rate and temperature dependent viscosity and heat conductivity. The model is expressed through a system of partial differential equations representing the balance of mass, the balance of linear momentum, the balance of energy and the equation for the entropy production. Assuming that we have Navier s slip at the impermeable boundary we establish the long-time existence of a (suitable) weak solution when the data are large. This result includes the classical Navier-Stokes-Fourier system for a Newtonean incompressible fluid with the viscosity and the heat conductivity depending on the temperature as a special case. The talk is based on joint works with M. Bulicek, E. Feireisl and K. R. Rajagopal.
17:20
 Prof. em. Dr.-Ing. Dr. h.c. Wolfgang L. Wendland (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart): Boundary Integral Equations and Pseudodifferential Operators (lecture 6 of 6)
 3.12.2007
15:40
 Prof. Bob (R. S.) Anderssen (CSIRO Mathematical and Information Sciences, Canberra): The Double Clumping Model of Wheat-Flour Dough Extension Abstract: The response of a wheat-flour dough to the flow and deformation performed on it during mixing is a sequence of hysteretic extension-rupture-recoil-relax events. On recording mixers, such as the Farinograph and Mixograph, this sequence of events is clearly visible in high resolution recordings. Because of its pin arrangement, the viscoelastic flow of the dough is simplest in the Mixograph and the upward branches of the stress-strain hysteretic events can be recovered. The importance of these upward branches is that they can be viewed as in situ measurements of the extensional flow of a dough, which is normally assessed using an extensograph to record the extensional flow (as an extensogram) of a dough sample taken from the mixer at a particular stage of the mixing. Traditionally, extensograph testing is utilized as a plant breeding assay to assess whether the flour from a new wheat variety will make a good bread or cake. The models, on which such deliberations are based, are rules-of-thumb correlations between the global structure of extensograms and the baking performance of good breads and cakes. In many ways, the rules-of-thumb simply reduce to being indirect measurements of the protein content of wheat-fours. From the baker?s perspective, extensograph testing, in conjunction with the rules-of-thumb, can be used to determine the optimal blending of expensive (high protein) and inexpensive (low protein) flours to achieve a given bread or cake quality. A major goal of plant breeding is the development of technology which will allow a new variety to be bred in three to five years rather than five to ten years. This can only be achieved if a more definitive understanding is available about the relationship between the molecular genetics of wheat-flours and the quality of the breads or cakes that they produce. This leads naturally to the need to understand the molecular dynamics of a dough during an extensograph test.
 10.12.2007
15:40
 Mgr. Miroslav Bulicek, Ph.D. (Mathematical Institut, Charles University, Prague): On existence of solution to incompressible Navier-Stokes-Fourier system with nonlinear heat flux and Cauchy stress Abstract: We derive under which assumptions on Cauchy stress and heat flux (both of them can be nonlinear functions of velocity gradient and temperature gradient, respectively) one has apriori estimates so strong that the definition of weak solution is meaningful. In addition, if we assume some monotonictity properties of Cauchy stress and heat flux we establish the existence of weak solution to N-S-F system whenever the weak formulation makes a good sense.
17:20
 Mgr. Miroslav Bulicek, Ph.D. (Mathematical Institute of Charles University, Prague): On existence of solution to heat equation with nonlinear heat flux, $L^1$ right hand side and nonintegrable convective term Abstract: The exitence theory for heat equation with nonlinear flux with $L^1$ right hand side was established by using the so-called method of $L^{infty}$ truncation function (developed by Boccardo and Murat). However, if we assume that the convective term is nonintegrable one can not use this method. There is also second method, the so-called method of Lipschitz approximation, that perfectly works if flux has some $r-1$ growth and we have $r$-estimates. But for this problem such estimates are not available. We show that a delicate combination of both methods leads to the proof of point-wise convergence of temperature gradient.
 17.12.2007
15:30
Prof. Dr. Eberhard Zeidler
(Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany):
Euler and the mathematical principles of modern natural philosophy I, II
Abstract:

## !!! Special memorial seminar, starts at 15:30 at the Building of the Faculty of Mathematics and Physics at Malostranska square 25. !!!

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