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Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: existence and uniqueness ×

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Now showing 1 - 2 of 2
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    On a thermomechanical model of phase transitions in steel
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Chełminski, Krzysztof; Hömberg, Dietmar; Kern, Daniela
    We investigate a thermomechanical model of phase transitions in steel. The strain is assumed to be additively decomposed into an elastic and a thermal part as well as a contribution from transformation induced plasticity. The resulting model can be viewed as an extension of quasistatic linear thermoelasticity. We prove existence of a unique solution and conclude with some numerical simulations.
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    Well-posedness of space and time dependent transport equations on a network
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Roggensack, Arne
    This article is concerned with the study of weak solutions of a linear transport equation on a bounded domain with coupled boundary data for general non smooth space and time dependent velocity elds. The existence of solutions, its uniqueness and the continuous dependence of the solution on the initial and boundary data as well on the velocity is proven. The results are based on the renormalization property. At the end, the theory is shown to be applicable to the continuity equation on a network.