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Author: Roggensack, Arne ×

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    Existence of weak solutions for the Cahn-Hilliard reaction model including elastic effects and damage
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Kraus, Christiane; Roggensack, Arne
    In this paper, we introduce and study analytically a vectorial Cahn-Hilliard reaction model coupled with rate-dependent damage processes. The recently proposed Cahn-Hilliard reaction model can e.g. be used to describe the behavior of electrodes of lithium-ion batteries as it includes both the intercalation reactions at the surfaces and the separation into different phases. The coupling with the damage process allows considering simultaneously the evolution of a damage field, a second important physical effect occurring during the charging or discharging of lithium-ion batteries. Mathematically, this is realized by a Cahn-Larché system with a non-linear Newton boundary condition for the chemical potential and a doubly non-linear differential inclusion for the damage evolution. We show that this system possesses an underlying generalized gradient structure which incorporates the non-linear Newton boundary condition. Using this gradient structure and techniques from the field of convex analysis we are able to prove constructively the existence of weak solutions of the coupled PDE system.
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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.