. . . . . . "Slab\u00E9 a siln\u00E9 principy maxima pat\u0159\u00ED k fundament\u00E1ln\u00EDm vlastnostem line\u00E1rn\u00EDch eliptick\u00FDch a parabolick\u00FDch parci\u00E1ln\u00EDch diferenci\u00E1ln\u00EDch rovnic druh\u00E9ho \u0159\u00E1du. Tyto principy mimo jin\u00E9 umo\u017E\u0148uj\u00ED porovnat dv\u011B r\u016Fzn\u00E1 \u0159e\u0161en\u00ED line\u00E1rn\u00EDch parci\u00E1ln\u00EDch rovnic v\u00FD\u0161e uveden\u00E9ho typu. Tyto principy lze pom\u011Brn\u011B snadno pou\u017E\u00EDt i pro semiline\u00E1rn\u00ED parci\u00E1ln\u00ED diferenci\u00E1ln\u00ED rovnice. Jednou z dosud nevy\u0159e\u0161en\u00FDch ot\u00E1zek je, zda tyto principy plat\u00ED tak\u00E9 pro siln\u011B neline\u00E1rn\u00ED singul\u00E1rn\u00ED nebo degenerovan\u00E9 parabolick\u00E9 \u010Di eliptick\u00E9 parci\u00E1ln\u00ED diferenci\u00E1ln\u00ED rovnice druh\u00E9ho \u0159\u00E1du. Pomoc\u00ED t\u011Bchto princip\u016F lze pak studovat jednozna\u010Dnost \u0159e\u0161en\u00ED \u00FAloh pro tyto rovnice. Hlavn\u00EDm c\u00EDlem projektu je identifikovat dostate\u010Dn\u011B \u0161irok\u00E9 t\u0159\u00EDdy rovnic, pro kter\u00E9 lze tyto principy dok\u00E1zat. Bude p\u0159ihl\u00ED\u017Eeno k tomu, aby podm\u00EDnky kladen\u00E9 na tyto t\u0159\u00EDdy rovnic byly dostate\u010Dn\u011B obecn\u00E9, aby byly splniteln\u00E9 v p\u0159\u00EDpadech d\u016Fle\u017Eit\u00FDch pro technickou praxi. Hlavn\u00ED metodika bude spo\u010D\u00EDvat ve vhodn\u00E9 volb\u011B testovac\u00EDch funkc\u00ED a pou\u017Eit\u00ED r\u016Fzn\u00FDch variant zobecn\u011Bn\u00E9 Gaussovy-Greenovy v\u011Bty. Abychom dos\u00E1hli po\u017Eadovan\u00FDch c\u00EDl\u016F, bude t\u0159eba v\u00FD\u0161e uveden\u00E9 techniky v\u00EDce rozpracovat a zjemnit. Mimo jin\u00E9 bychom se v projektu cht\u011Bli zam\u011B\u0159it na t\u0159\u00EDdu p-homogenn\u00EDch \u00FAloh z hydrodynamiky tekutiny prosakuj\u00EDc\u00ED hr\u00E1z\u00ED z por\u00E9zn\u00EDho materi\u00E1lu (nap\u0159.betonu) v\u010Detn\u011B p\u0159\u00EDpadu stacion\u00E1rn\u00EDho proud\u011Bn\u00ED. Zku\u0161en\u00FDm \u0159e\u0161itel\u016Fm projektu (Dr\u00E1bek, Girg, Tak\u00E1\u010D) se poda\u0159ilo publikovat citovan\u00E9 v\u00FDsledky ohledn\u011B \u0159e\u0161itelnosti pro stacion\u00E1rn\u00ED p\u0159\u00EDpad v \u0159ad\u011B spole\u010Dn\u00FDch publikac\u00ED." . "Fundamental qualitative properties of degenerated and singular parabolic differential equations"@en . . "Fundament\u00E1ln\u00ED kvalitativn\u00ED vlastnosti degenerovan\u00FDch a singul\u00E1rn\u00EDch parabolick\u00FDch diferenci\u00E1ln\u00EDch rovnic" . . . "0"^^ . "0"^^ . " comparison principles" . "maximum principles" . "1"^^ . "0"^^ . "2014-03-28+01:00"^^ . "Weak and strong maximum principles are fundamental properties of linear elliptic and parabolic partial differential equations of the second order. Using these principles, one can compare two different solutions of linear partial differential equations of the afforementioned type. These principles can be also easily applied to semilinear partial differential equations of second order. One very important open question concerns validity of these fundamental principles for strongly nonlinear singular or degenerated parabolic and/or elliptic partial differential equations of the second order. If these principles are valid, then among other things, one can use them to prove the uniqueness of the solution of these problems. Note that the uniqueness of solutions plays an important role in the numerical treatment of the problems as well as it is very important in technical and other scientific applications. Thus the positive answer to this open question would be a great contribution to the applicable theory of these kind of problems. Our main goal consists in identification of sufficiently wide class of problems for which these principles hold."@en . . "0"^^ . . "2015-05-28+02:00"^^ . "2014-02-01+01:00"^^ . . "2015-12-31+01:00"^^ . . . . . "http://www.isvav.cz/projectDetail.do?rowId=7AMB14DE005"^^ . "7AMB14DE005" . . "maximum principles; comparison principles; parabolic and elliptic partial differential equations"@en .