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Author: Sprekels, Jürgen × Author: Wu, Hao × Type: Text × Type: report ×

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Now showing 1 - 3 of 3
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    Optimal distributed control of a Cahn-Hilliard-Darcy system with mass sources
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Sprekels, Jürgen; Wu, Hao
    In this paper, we study an optimal control problem for a two-dimensional CahnHilliardDarcy system with mass sources that arises in the modeling of tumor growth. The aim is to monitor the tumor fraction in a finite time interval in such a way that both the tumor fraction, measured in terms of a tracking type cost functional, is kept under control and minimal harm is inflicted to the patient by administering the control, which could either be a drug or nutrition. We first prove that the optimal control problem admits a solution. Then we show that the control-to-state operator is Fréchet differentiable between suitable Banach spaces and derive the first-order necessary optimality conditions in terms of the adjoint variables and the usual variational inequality.
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    Elastoplastic Timoshenko beams
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Krejčí, Pavel; Sprekels, Jürgen; Wu, Hao
    A Timoshenko type elastoplastic beam equation is derived by dimensional reduction from a general 3D system with von Mises plasticity law. It consists of two second-order hyperbolic equations with an anisotropic vectorial Prandtl--Ishlinskii hysteresis operator. Existence and uniqueness of a strong solution for an initial-boundary value problem is proven via standard energy and monotonicity methods.
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    A note on a parabolic equation with nonlinear dynamical boundary condition
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Sprekels, Jürgen; Wu, Hao
    We consider a semilinear parabolic equation subject to a nonlinear dynamical boundary condition that is related to the so-called Wentzell boundary condition. First, we prove the existence and uniqueness of global solutions as well as the existence of a global attractor. Then we derive a suitable Lojasiewicz-Simon type inequality to show the convergence of global solutions to single steady states as time tends to infinity under the assumption that the nonlinear terms f, g are real analytic. Moreover, we provide an estimate for the convergence rate.