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Author: Wu, Hao × Type: Text ×

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Now showing 1 - 5 of 5
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    Global strong solutions of the full Navier-Stokes and Q-tensor system for nematic liquid crystal flows in 2D: Existence and long-time behavior
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Cavaterra, Cecilia; Rocca, Elisabetta; Wu, Hao; Xu, Xiang
    We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter xi that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate.
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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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    Asymptotic behavior of a hydrodynamic system in the nematic liquid crystal flows
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Liu, Chun; Wu, Hao; Xu, Xiang
    In this paper we study the long time behavior of the classical solutions to a hydrodynamical system modeling the flow of nematic liquid crystals. This system consists of a coupled system of Navier--Stokes equations and kinematic transport equations for the molecular orientations. By using a suitable Lojasiewicz--Simon type inequality, we prove the convergence of global solutions to single steady states as time tends to infinity. Moreover, we provide estimates for the convergence rate.
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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.