. . "5"^^ . . . "5"^^ . . "2014-04-18+02:00"^^ . "http://www.isvav.cz/projectDetail.do?rowId=GAP201/12/1757"^^ . "GAP201/12/1757" . "Analysis of underlying discrete and continuous structures in ordinary and partial differential equations has recently attracted a lot of attention. The motivation is not only theoretical (distinct behavior, e.g. stability or chaos) but also practical (numerical approximation of ODEs and PDEs) and applied (comparison of corresponding biological or economical models). The goal of this project is to study PDEs on continuous-discrete domains. We would like to follow and extend approaches like semidiscrete methods in numerical analysis or Rothe's method in analysis. In contrast to these well-known methods, which concentrate mainly on convergence issues, our main contribution should be the study of solutions on general domains. Furthermore, we intend to describe its possible applications, e.g. in stochastic processes and probability theory."@en . . . . . . . . "The scientific contribution of the project lies in deriving new properties of partial differential equations on lattices and their dependence on the considered time structure, in the description of their connection with stochastic processes and with evolutionary games on graphs. The results of the project are published in 6 scientific papers (5 published and 1 submitted)."@en . "Partial differential equations on continuous-discrete domains"@en . "0"^^ . . . "Odborn\u00FD p\u0159\u00EDnos projektu je v odvozen\u00ED nov\u00FDch vlastnost\u00ED parci\u00E1ln\u00EDch diferenci\u00E1ln\u00EDch rovnic na m\u0159\u00ED\u017Ek\u00E1ch a jejich z\u00E1vislosti na uva\u017Eovan\u00E9 \u010Dasov\u00E9 struktu\u0159e, v popisu jejich souvislosti se stochastick\u00FDmi procesy a s evolu\u010Dn\u00EDmi hrami na grafech. V\u00FDstupy projektu jsou seps\u00E1ny do 6 odborn\u00FDch publikac\u00ED (z nich\u017E 5 vy\u0161lo a 1 je v recenzn\u00EDm \u0159\u00EDzen\u00ED)."@cs . "0"^^ . "Anal\u00FDza diskrt\u00E9n\u00EDch a spojit\u00FDch struktur na pozad\u00ED oby\u010Dejn\u00FDch a parci\u00E1ln\u00EDch diferenci\u00E1ln\u00EDch rovnic p\u0159itahuje v posledn\u00ED dob\u011B st\u00E1le v\u00EDce pozornosti. D\u016Fvody jsou teoretick\u00E9 (odli\u0161n\u00E9 chov\u00E1n\u00ED, nap\u0159. stabilita a chaos), praktick\u00E9 (numerick\u00E1 aproximace) i aplikovan\u00E9 (biologick\u00E9 a ekonomick\u00E9 modely). C\u00EDlem tohoto projektu je studium parci\u00E1ln\u00EDch diferenci\u00E1ln\u00EDch rovnic na spojit\u011B-diskr\u00E9tn\u00EDch oblastech. R\u00E1di bychom n\u00E1sledovali a roz\u0161\u00ED\u0159ili p\u0159\u00EDstupy jako semidiskr\u00E9tn\u00ED metody v numerick\u00E9 anal\u00FDze nebo Rotheho metodu v matematick\u00E9 anal\u00FDze. Na rozd\u00EDl od t\u011Bchto zn\u00E1m\u00FDch metod, kter\u00E9 se soust\u0159ed\u00ED zejm\u00E9na na konvergenci, n\u00E1\u0161 hlavn\u00ED p\u0159\u00EDnos by m\u011Bla b\u00FDt podrobn\u00E1 anal\u00FDza \u0159e\u0161en\u00ED na obecn\u00FDch struktur\u00E1ch. D\u00E1le bychom r\u00E1di popsali mo\u017En\u00E9 aplikace, nap\u0159\u00EDklad ve stochastick\u00FDch procesech a teorii pravd\u011Bpodobnosti." . . "Parci\u00E1ln\u00ED diferenci\u00E1ln\u00ED rovnice na spojit\u011B-diskr\u00E9tn\u00EDch oblastech" . "1"^^ . . "2015-05-22+02:00"^^ . "2014-12-31+01:00"^^ . . "2012-01-01+01:00"^^ . . "partial differential equations difference equations time scales stochastic processes"@en .