"US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . "609282" . "Prandtl-Ishlinskii operaor, Homogenization, Heat equation"@en . "Homogenization of heat equation with hysteresis"@en . "Mathematics and Computers in Simulation" . . "61" . "Homogenization of heat equation with hysteresis" . "26210" . "Homogenization of heat equation with hysteresis"@en . "[D6332FA2A8FD]" . "RIV/00216305:26210/03:PU40864!RIV/2005/GA0/262105/N" . "P\u0159\u00EDsp\u011Bvek se zab\u00FDv\u00E1 rovnic\u00ED veden\u00ED tepla ve tvaru (c u+W[u])_t=div(a.grad u)=f, kde function\u00E1ln\u00ED oper\u00E1tor W[u] je Prandtl\u016Fv-Ishlinsk\u00E9ho hyster\u00E9zn\u00ED oper\u00E1tor typu play charakterizov\u00E1n\u00FD distribu\u010Dn\u00ED funct\u00ED eta. Je studov\u00E1na prostorov\u011B z\u00E1visl\u00E1 po\u010D\u00E1te\u010Dn\u00ED okrajov\u00E1 \u00FAloha. D\u016Fkaz existence a jednozna\u010Dnosti \u0159e\u0161en\u00ED je vynech\u00E1n, proto\u017Ee d\u016Fkaz je lehkou modifikac\u00ED d\u016Fkazu Brokate a Sprekelse. Je \u0159e\u0161ena \u00FAloha homogenizace t\u00E9to rovnice. Pro eps->0, uva\u017Eujeme posloupnost \u00FAloh uveden\u00E9ho tvaru s prostorov\u011B eps-periiodick\u00FDmi koeficienty c^eps, eta^eps, a^eps. Koefficienty c^star,eta^star a a^star v homogenizovan\u00E9 \u00FAloze jsou identifikov\u00E1ny a konvergence p\u0159\u00EDslu\u0161n\u00FDch \u0159e\u0161en\u00ED u^eps k u^star je dok\u00E1z\u00E1na."@cs . . . . "0378-4754" . "591-597" . "Homogenization of heat equation with hysteresis" . "Homogenizace rovnice veden\u00ED tepla s hysterez\u00ED"@cs . . "7"^^ . . . "Homogenizace rovnice veden\u00ED tepla s hysterez\u00ED"@cs . . . . "The contribution delas with heat equaition in the form (c u+W[u])_t=div(a.grad u)=f, where the functional operator W[u] is Prandtl-Ishlinskii hysteresis operator of play type characterized by a distribution function eta. The spatially dependent initial boundary value problem is studied. Proof of existence and uniqueness of the solution is omitted since the proof is a slightly modified proof by Brokate-Sprekels. The homogenization problem for this equation si studied. For eps->0, a sequence of pproblems of the above type with spatially eps-periodic coefficients c^eps, eta,^eps, a^eps si considered. The coefficients c^star,eta^star and a^star in the homogenized problem are identified and convergence of the corresponding solutions u^eps to u^star is proved."@en . . "Franc\u016F, Jan" . "The contribution delas with heat equaition in the form (c u+W[u])_t=div(a.grad u)=f, where the functional operator W[u] is Prandtl-Ishlinskii hysteresis operator of play type characterized by a distribution function eta. The spatially dependent initial boundary value problem is studied. Proof of existence and uniqueness of the solution is omitted since the proof is a slightly modified proof by Brokate-Sprekels. The homogenization problem for this equation si studied. For eps->0, a sequence of pproblems of the above type with spatially eps-periodic coefficients c^eps, eta,^eps, a^eps si considered. The coefficients c^star,eta^star and a^star in the homogenized problem are identified and convergence of the corresponding solutions u^eps to u^star is proved." . "P(GA201/00/0557)" . "RIV/00216305:26210/03:PU40864" . "3-5" . "1"^^ . . . "1"^^ .