. "16"^^ . "16"^^ . . . . . "Bylo dosa\u017Eeno nov\u00FDch kvalitativn\u00EDch v\u00FDsledk\u016F o asymptotick\u00E9m chov\u00E1n\u00ED nekone\u010Dn\u011B rozm\u011Brn\u00FDch dynamick\u00FDch syst\u00E9m\u016F: Kompaktnost mno\u017Einy \u0159e\u0161en\u00ED a existence glob\u00E1ln\u00EDch \u0159e\u0161en\u00ED, konvergence \u0159e\u0161en\u00ED k rovnov\u00E1\u017En\u00E9mu stavu a \u00FAlohy s rychle osciluj\u00EDc\u00ED hranic\u00ED."@cs . "0"^^ . . . . "2009-07-02+02:00"^^ . . "The proposed research project represents a continuation of a general programme of investigation of the qualitative properties of infinite-dimensional dynamical systems. Recently, the authors of the project developed the theory in two directions: Mathematical models of phase transition phenomena, and the asymptotic properties of solutions of the equations of fluid dynamics. Among the main achievements, there are two general methods applicable to a large variety of problems. The first consists in using the so-called defect measures in the study of asymptotically compact dynamical systems while the second leans on a generalization of the Lojasiewicz-Simon method to non-smooth functionals. The goal of the present project is to develop these tools to attack the problems lying beyond the scope of applicability of standard methods based on the concept of compactness of the underlying solution semigroup. Typical examples are hyperbolic-parabolic systems and equations with non-local operators."@en . "New qualitative results concerning the asymptotic behavior of infinite-dimensional dynamical systems have been achieved: Compactness of solutions and global existence, convergence towards equilibria, and problems with rapidly oscillating boundaries."@en . . "0"^^ . . "2008-12-31+01:00"^^ . "IAA100190606" . . "1"^^ . "http://www.isvav.cz/projectDetail.do?rowId=IAA100190606"^^ . . "2008-02-21+01:00"^^ . "2006-01-01+01:00"^^ . "Asymptotick\u00E1 anal\u00FDza nekone\u010Dn\u011B dimension\u00E1ln\u00EDch dynamick\u00FDch syst\u00E9m\u016F" . . "Navrhovan\u00FD projekt je pokra\u010Dov\u00E1n\u00EDm obecn\u00E9ho v\u00FDzkumn\u00E9ho programu vy\u0161et\u0159ov\u00E1n\u00ED kvalitativn\u00EDch vlastnost\u00ED nekone\u010Dn\u011B rozm\u011Brn\u00FDch dynamick\u00FDch syst\u00E9m\u016F. V ned\u00E1vn\u00E9 dob\u011B se autor\u016Fm projektu poda\u0159ilo rozvinout teorii ve dvou sm\u011Brech: Matematick\u00E9 modely f\u00E1zov\u00FDch p\u0159echod\u016F a asymptotick\u00E9 vlastnosti \u0159e\u0161en\u00ED rovnic hydrodynamiky. Byly odvozeny dv\u011B nov\u00E9 metody pou\u017Eiteln\u00E9 pro \u0161irokou t\u0159\u00EDdu probl\u00E9m\u016F. Prvn\u00ED z nich spo\u010D\u00EDv\u00E1 ve vyu\u017Eit\u00ED tzv. defektn\u00EDch m\u011Br p\u0159i studiu asymptoticky kompaktn\u00EDch dynamick\u00FDch syst\u00E9m\u016F, zat\u00EDmco druh\u00E1 je zalo\u017Eena na zobecn\u011Bn\u00ED Lojasiewiczovy Simonovy metody na obecn\u00E9 nehladk\u00E9 funkcion\u00E1ly. C\u00EDlem projektu je rozvinut\u00ED t\u011Bchto metod na \u00FAlohy, kter\u00E9 le\u017E\u00ED za hranicemi pou\u017Eitelnosti standardn\u00EDch postup\u016F zalo\u017Een\u00FDch na pojmu kompaktnosti \u0159e\u0161\u00EDc\u00ED semigrupy. Typick\u00FDmi p\u0159\u00EDklady jsou hyperbolicko-parabolick\u00E9 syst\u00E9my a rovnice obsahuj\u00EDc\u00ED nelok\u00E1ln\u00ED oper\u00E1tory." . " asymptotic behaviour" . . . . . "Dynamical system; asymptotic behaviour; evolutionary equation"@en . "Dynamical system" . "Asymptotic analysis of infinite-dimensional dynamical systems"@en .