"Matematick\u00E9 modelov\u00E1n\u00ED n\u011Bkter\u00FDch neline\u00E1rn\u00EDch probl\u00E9m\u016F mechaniky kontinua" . . . "12"^^ . "1"^^ . "12"^^ . . "0"^^ . . . . . "0"^^ . . . . . "Mathematical modelling of some nonlinear problems in continuum mechanics"@en . . . "GA201/97/0153" . . "N\u00E1m\u011Btov\u011B rozs\u00E1hl\u00FD projekt, v jeho\u017E r\u00E1mci bylo ur\u010Deno 5 t\u00E9mat, spadaj\u00EDc\u00EDch do okruhu neline\u00E1rn\u00EDch probl\u00E9m\u016F mechaniky kontinua. Z\u00EDsk\u00E1ny p\u016Fvodn\u00ED teoretick\u00E9 v\u00FDsledky zejm\u00E9na v oboru konvek\u010Dn\u011B-dif\u00FAzn\u00EDch rovnic, metod homogenizace v \u00FAloh\u00E1ch s hystenz\u00ED a numeri"@cs . "The main aim of the first and third themes is development of methods of solving convection - diffusion problems. The first case concerns problems of Stefan tape with convective term and nonlinear and degenerate diffusion ( a motive : continuous casting of steel ). The convective term considerably prevails the diffusion term near the interface, separating the liquid and solid phases, and thus difficultes of solving increase significantly. The third theme concernsnumerical solving Navier-Stokes and Eulerequations. A special attention will be devoted to constructing a robus scheme for Euler equations. In both themes a convenient implementationof the method of characteristics will be used. The second theme is mathematical modelling of hysteresis material s with perodic coefficients and hysteresis operator. The aim is a homogenization of these equations and development of corresponding numerical methods."@en . "http://www.isvav.cz/projectDetail.do?rowId=GA201/97/0153"^^ . "Hlavn\u00EDm c\u00EDlem prvn\u00EDho a t\u0159et\u00EDho t\u00E9matu je rozvijen\u00ED metod \u0159e\u0161en\u00ED konvek\u010Dn\u011B - difuzn\u00EDch \u00FAloh. V prvn\u00EDm p\u0159\u00EDpad\u011B jde o \u00FAlohy Stefanova typu s konvektivn\u00EDm \u010Dlenem a neline\u00E1rn\u00ED a degenerovanou difuz\u00ED (motivace : spojit\u00E9 lit\u00ED kov\u016F). Konvektivn\u00ED \u010Dlen p\u0159evy\u0161uje v oblasti rozhran\u00ED mezi pevnou a tekutou f\u00E1z\u00ED difuzn\u00ED \u010Dlen a tak se podstatn\u011B zvy\u0161uje n\u00E1ro\u010Dnost \u0159e\u0161en\u00ED. V t\u0159et\u00EDm t\u00E9matu jde o numerick\u00E9 \u0159e\u0161en\u00ED Navier - Stokesov\u00FDch resp. Eulerov\u00FDch rovnic. Speci\u00E1ln\u00ED pozornost bude v\u011Bnov\u00E1na konstrukci robustn\u00ED metody pro Eulerovy rovnice. V obou t\u00E9matech se jedn\u00E1 o vhodnou implementaci metody charakteristik. Druh\u00FDm t\u00E9matem je matematick\u00E9 modelov\u00E1n\u00ED hysterezn\u00EDch materi\u00E1l\u016F s periodickou struktorou pomoc\u00ED diferenci\u00E1ln\u00EDch rovnic, kter\u00E1 je nutn\u00E1 pro numerick\u00E1 v\u00FDpo\u010Dty, av\u00FDvoj p\u0159\u00EDslu\u0161n\u00FDch numerick\u00FDch metod." .