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Author: Sprekels, Jürgen × End date: 2009 × Start date: 2004 × Type: Text ×

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Now showing 1 - 9 of 9
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    Small strain oscillations of an elastoplastic Kirchhoff plate
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Guenther, Ronald B.; Krejčí, Pavel; Sprekels, Jürgen
    The two dimensional equation for transversal vibrations of an elastoplastic plate is derived from a general three dimensional system with a single yield tensorial von Mises plasticity model in the five dimensional deviatoric space. It leads after dimensional reduction to a multiyield three dimensional Prandtl-Ishlinskii hysteresis model whose weight function is explicitly given. The resulting partial differential equation with hysteresis is solved by means of viscous approximations and a monotonicity argument.
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    A nonlocal phase-field model with nonconstant specific heat
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Krejčí, Pavel; Rocca, Elisabetta; Sprekels, Jürgen
    We prove the existence, uniqueness, thermodynamic consistency, global boundedness from both above and below, and continuous data dependence for a strong solution to an integrodifferential model for nonisothermal phase transitions under nonhomogeneous mixed boundary conditions. The specific heat is allowed to depend on the order parameter, and the convex component of the free energy may or may not be singular.
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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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    An optimal control approach to curved rods
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Sprekels, Jürgen; Tiba, Dan
    In this paper, a new approach to the generalized Naghdi model for the deformation of three-dimensional curved rods is studied. The method is based on optimal control theory.
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    The von Mises model vor one-dimensional elastoplastic beams and Prandtl-Ishlinskii hysteresis operators
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Krejčí, Pavel; Sprekels, Jürgen
    In this paper, the one-dimensional equation for the transversal vibrations of an elastoplastic beam is derived from a general three-dimensional system. The plastic behavior is modeled using the classical three-dimensional von Mises plasticity model. It turns out that this single-yield model without hardening leads after a dimensional reduction to a multi-yield one-dimensional hysteresis model with kinematic hardening, given by a hysteresis operator of Prandtl-Ishlinskii type whose density function can be determined explicitly. This result indicates that the use of Prandtl-Ishlinskii hysteresis operators in the modeling of elastoplasticity is not just a questionable phenomenological approach, but in fact quite natural. In addition to the derivation of the model, it is shown that the resulting partial differential equation with hysteresis can be transformed into an equivalent system for which the existence and uniqueness of a strong solution is proved. The proof employs techniques from the mathematical theory of hysteresis operators.
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    Optimal boundary control of a phase field system modeling nonisothermal phase transitions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Lefter, Catalin; Sprekels, Jürgen
    In this paper, we study an optimal control problem for a singular system of partial differential equations that models a nonisothermal phase transition with a nonconserved order parameter. The control acts through a third boundary condition for the absolute temperature and plays the role of the outside temperature. It is shown that the corresponding control-to-state mapping is well defined, and the existence of an optimal control and the first-order optimality conditions for a quadratic cost functional of Bolza type are established.
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    Optimal control of 3D state constrained induction heating problems with nonlocal radiation effects
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Druet, Pierre-Étienne; Klein, Olaf; Sprekels, Jürgen; Tröltzsch, Fredi; Yousept, Irwin
    The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperature-dependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove the existence and uniqueness of the solution to the state equation. The regularity analysis associated with the time harmonic Maxwell equations is also studied. In the second part of the paper, the existence and uniqueness of the solution to the corresponding linearized equation is shown. With this result at hand, the differentiability of the control-to-state mapping operator associated with the state equation is derived. Finally, based on the theoretical results, first oder necessary optimality conditions for an associated optimal control problem are established.
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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.