Grant-funded Project Nr. 006/2005/R/MFF
Final Report

Project title:Nonlinear models in continuum mechanics
Research leader:Mgr. Martin Lanzendörfer, 2003
Co-researcher: doc. RNDr. Josef Málek, CSc.; RNDr. Martin Mádlík, 2004; RNDr. Iveta Hnětynková, 2003; Mgr. Jan Stebel, 2004; Mgr. Miroslav Bulíček, 2003; Mgr. Lukáš Poul, 2004; Mgr. Petr Šedivý, 2004; Mgr. Václav Kučera, 2004; Mgr. Miroslav Pošta, 2004; Mgr. Vít Průša, 2004
Period of project:2005-2006
Overall grant:1200 000 CZK

Project Results

The main goal of the project was to create and support a team of 10 doctoral students recruited from 3 different study programs (Mathematical analysis, Scientific and technical computation, Mathematical and computer modelling) on MFF UK, the research interests of those were focused on problems of mathematical and computational modelling in continuum mechanics - namely of the flow of an incompressible non-Newtonian fluid, flow of a compressible Navier-Stokes fluid, the problem of their control and optimization and the problem of fluid-structure interaction.

In order to reach the goals, the following activities have been realized:
- five lecture series and intensive courses of invited specialists, two domestic and eight foreign, were organised, see the attachment
- regular meetings of the project team were kept, including presentations of the progress of their research
- collective participation of the students on international conferences, schools or workshops were supported, see the attachment.

Supported by the project, M. Bulíček and I. Hnětynková have succesfully defended their doctoral theses already; other students (J. Stebel, V. Průša, L. Poul, V. Kučera, M. Lanzendörfer) are finishing their work, planning to defend by year 2007, the others in year 2008.

In high quality international scientific journals 3 articles were published, 4 posters and 51 oral contributions were presented on conferences, including one invited talk. Of these, 11 papers were published in the conference proceedings, see the attachment.

Software for numerical simulations of some particular continuum mechanics problems have been implemented, see the attachment.

Students succesfully join the research effort either at MFF UK, or at other institutions (Nečas Center for Mathematical Modelling, Mathematical Institute AS CR, Institute of Computer Science AS CR)

List of more important publications:
* L. Poul: Asymptotic behaviour of solutions of quasilinear evolutionary partial differential equations of parabolic type on unbounded spatial intervals. Math. Methods Appl. Sci. 29, No. 9, 1035-1051 (2006). (IF 0.526)
* M. Bulíček, J. Málek, K. R. Rajagopal: Navier's Slip and Evolutionary Navier-Stokes-Like Systems with Pressure and Shear-rate Dependent Viscosity, Indiana Univ. Math. J., Vol. 56, No. 1 (2007) (IF 0.769)
* V. Průša: Sufficient Conditions for Monotone Linear Stability of Steady and Oscillatory Hagen-Poiseuille Flow. SIAM J. Appl. Math., Vol. 67, No. 2, 354-363 (2007). (IF 1.120)