"Compatibility of dynamics and statics in multicomponent dissipative systems"@en . "2007-09-26+02:00"^^ . . "Souhlas dynamick\u00FDch a statick\u00FDch jev\u016F ve v\u00EDceslo\u017Ekov\u00FDch disipativn\u00EDch syst\u00E9mech" . . "http://www.isvav.cz/projectDetail.do?rowId=IAA1019302"^^ . . "1"^^ . . "partial differential equation" . . . . . "0"^^ . "partial differential equation; asymtotic behaviour; dissipative dynamical system"@en . "projekt se zab\u00FDv\u00E1 asymptotick\u00FDm chov\u00E1n\u00EDm \u0159e\u0161en\u00ED parci\u00E1ln\u00EDch diferenci\u00E1ln\u00EDch rovnic, kter\u00E9 modeluj\u00ED v\u00EDceslo\u017Ekov\u00E9 dynamick\u00E9 syst\u00E9my. T\u011B\u017Ei\u0161t\u011Bm projektu jsou zejm\u00E9na ot\u00E1zky chov\u00E1n\u00ED \u0159e\u0161en\u00ED pro dlouh\u00E9 \u010Dasy a korvengence ke klidov\u00E9mu stavu. Konkr\u00E9tn\u011B jsou navrhov\u00E1ny t\u0159i z\u00E1klad\u00ED okruhy \u00FAloh:1. Rovnice popisuj\u00EDc\u00ED pohyb jednoho nebo v\u00EDce tuh\u00FDch t\u011Bles ve viskozn\u00ED tekutin\u011B. 2. Rovnice modeluj\u00EDc\u00ED f\u00E1zov\u00E9 p\u0159echody mezi pevn\u00FDmi l\u00E1tkami a kapalinami. 3. Modely s konvexn\u00ED strukturou v teorii f\u00E1zov\u00FDch p\u0159echod\u016F v pevn\u00FDch l\u00E1tk\u00E1ch. Pro ka\u017Ed\u00FD z uveden\u00FDch model\u016F budou zkoum\u00E1ny ot\u00E1zky existence a jednozna\u010Dnosti \u0159\u0159e\u0161en\u00ED, chov\u00E1n\u00ED \u0159e\u0161en\u00ED pro dlouh\u00E9 \u010Dasy, stabilizace \u0159e\u0161en\u00ED evolu\u010Dn\u00EDch \u00FAloh k \u0159e\u0161en\u00ED rovnic stacion\u00E1rn\u00EDch a struktura mno\u017Einy stacion\u00E1rn\u00EDch \u0159e\u0161en\u00ED." . "Byly dosa\u017Eeny nov\u00E9 teoretick\u00E9 v\u00FDsledky pro syst\u00E9my evolu\u010Dn\u00EDch diferenci\u00E1ln\u00EDch rovnic matematick\u00E9 fyziky: (1) rovnice dynamiky tekutin, (2) modely f\u00E1zov\u00E9ho pole, (3) chov\u00E1n\u00ED \u0159e\u0161en\u00ED t\u011Bchto model\u016F pro dlouh\u00E9 \u010Dasy."@cs . . . . . "14"^^ . "14"^^ . "The main topic of the project is to study the asymptotic behaviour of solution to partial differential aquations arising in multicomponent systems modelling. The long-time behaviour of solutions as well as the problem of stabilization towards a stationary state will be investigated. Specifically, the following systems are considered: 1. The equations describing the motion of one or several rigid bodies in a viscous fluid. 2. The solid-liquid phase field models. 3. Dynamical solid-solid phase transition models. In each specific situation, we shall study the existence and uniqueness of solutions, the long-time behaviour, stabilization to rest states, and the structure of the set of stationary solutions."@en . . "New theoretical results for systems of evolutionary differential equations arising in mathematical physics were obtained:"@en . . "IAA1019302" . . . . . " asymtotic behaviour" . . "0"^^ .