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Author: Heinemann, Christian × Subject: energetic solutions ×

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Now showing 1 - 3 of 3
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    Existence of weak solutions for a hyperbolic-parabolic phase field system with mixed boundary conditions on non-smooth domains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Heinemann, Christian; Kraus, Christiane
    The aim of this paper is to prove existence of weak solutions of hyperbolic-parabolic evolution inclusions defined on Lipschitz domains with mixed boundary conditions describing, for instance, damage processes and elasticity with inertial effects. To this end, we first present a suitable weak formulation in order to deal with such evolution inclusions. Then, existence of weak solutions is proven by utilizing time-discretization, H2-regularization and variational techniques.
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    Existence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Heinemann, Christian; Kraus, Christiane
    In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed boundary conditions for the displacement variable. The main aim of this work is to establish existence of weak solutions for the introduced hyperbolic-parabolic system. To this end, we first adopt the notion of weak solutions introduced in [HK11]. Then we prove existence of weak solutions by means of regularization, time-discretization and different variational techniques.
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    Modeling and analysis of a phase field system for damage and phase separation processes in solids
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bonetti, Elena; Heinemann, Christian; Kraus, Christiane; Segatti, Antonio
    In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an elliptic system with material dependent coefficients for the strain tensor and a doubly nonlinear differential inclusion for the damage function. The main aim of this paper is to show existence of weak solutions for the introduced model, where, in contrast to existing damage models in the literature, different elastic properties of damaged and undamaged material are regarded. To prove existence of weak solutions for the introduced model, we start with an approximation system. Then, by passing to the limit, existence results of weak solutions for the proposed model are obtained via suitable variational techniques.