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Author: Müller, Ingo × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik ×

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    Emergence of rate-independent dissipation from viscous systems with wiggly energies : dedicated to Ingo Müller on the occasion of his 75th birthday
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Mielke, Alexander; Müller, Ingo
    We consider the passage from viscous system to rate-independent system in the limit of vanishing viscosity and for wiggly energies. Our new convergence approach is based on the (R,R*) formulation by De Giorgi, where we pass to the Γ limit in the dissipation functional. The difficulty is that the type of dissipation changes from a quadratic functional to one that is homogeneous of degree 1. The analysis uses the decomposition of the restoring force into a macroscopic part and a fluctuating part, where the latter is handled via homogenization.
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    Distributed optimal control of a nonstandard system of phase field equations : dedicated to Prof. Dr. Ingo Müller on the occasion of his 75th birthday
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Colli, Pierluigi; Gilardi, Gianni; Podio-Guidugli, Paolo; Sprekels, Jürgen; Müller, Ingo
    We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been introduced recently in [4], on the basis of the theory developed in [15], and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.