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  • Příspěvek se zabývá rovnicí vedení tepla ve tvaru (c u+W[u])_t=div(a.grad u)=f, kde functionální operátor W[u] je Prandtlův-Ishlinského hysterézní operátor typu play charakterizováný distribuční functí eta. Je studována prostorově závislá počáteční okrajová úloha. Důkaz existence a jednoznačnosti řešení je vynechán, protože důkaz je lehkou modifikací důkazu Brokate a Sprekelse. Je řešena úloha homogenizace této rovnice. Pro eps->0, uvažujeme posloupnost úloh uvedeného tvaru s prostorově eps-periiodickými koeficienty c^eps, eta^eps, a^eps. Koefficienty c^star,eta^star a a^star v homogenizované úloze jsou identifikovány a konvergence příslušných řešení u^eps k u^star je dokázána. (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.
  • 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)
Title
  • Homogenizace rovnice vedení tepla s hysterezí (cs)
  • Homogenization of heat equation with hysteresis
  • Homogenization of heat equation with hysteresis (en)
skos:prefLabel
  • Homogenizace rovnice vedení tepla s hysterezí (cs)
  • Homogenization of heat equation with hysteresis
  • Homogenization of heat equation with hysteresis (en)
skos:notation
  • RIV/00216305:26210/03:PU40864!RIV/2005/GA0/262105/N
http://linked.open.../vavai/riv/strany
  • 591-597
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  • P(GA201/00/0557)
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  • 3-5
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  • 609282
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  • RIV/00216305:26210/03:PU40864
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  • Prandtl-Ishlinskii operaor, Homogenization, Heat equation (en)
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  • US - Spojené státy americké
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  • [D6332FA2A8FD]
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  • Mathematics and Computers in Simulation
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  • 61
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  • Franců, Jan
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  • 0378-4754
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  • 26210
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