Karl Kunisch’s research while affiliated with University of Graz and other places

... In particular a lack of equivalence with the stochastic interpretation is shown. In [8] a proof of well-posedness is given that drops the assumption of global Lipschitz continuity and in turn yields local results and [7] proposes a numerical realization based on a polynomial approximation of the value function. ...

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Local well-posedness of the minimum energy estimator for a defocusing cubic wave equation

... mean field games with multiple solutions [7], or mean-field game models for systemic risk [89]. Moreover, the impact of the proposed methodology expands well beyond the realm of physical multiagent systems to problems in computational statistics, where there is interest in accelerating convergence to the target distribution for Fokker-Planck dynamics in applications related to sampling from probability measures in high dimensions [27,28,90]. ...

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Computation and control of unstable steady states for mean field multiagent systems

... For instance, if f ∈ L 1 ((0, T ); L 2 (Ω; R 2 )) + L 2 ((0, T ); W −1,2 (Ω; R 2 )) then for any sufficiently regular v 0 there exists a unique so-called strong solution v of (1.1) with v(·, 0) = v 0 inter alia belonging to L 4 (Ω × (0, T ); R 2 ) [30, Theorem 4.2.1], and further well-posedness results for f ∈ L r ((0, T ); W −1,q (Ω; R 2 )) have been obtained in [3] for other choices of r and q as well. Moreover, [44, Proposition 1.1 and Proposition 1 .3] ...

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Uniform Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document} Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing

... While traditional methods like those in [62] and [63] emphasize computational efficiency and stability through finite difference and volume methods, the proposed approach offers a novel perspective by integrating the Bellman dynamic programming principle with nonlinear minimization techniques [64]. Additionally, unlike the tensor decomposition and deep learning methods that address high-dimensional challenges [65,66], the proposed method provides a more direct computational strategy for nonlinear problems, potentially offering more precise control solutions under certain smooth assumptions. The proposed approach complements existing works by providing an alternative pathway to achieving optimal feedback control, particularly in scenarios where traditional numerical methods may face limitations. ...

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On the Hamilton–Jacobi-Bellman approach to the relaxed optimal feedback control problems

... • Another aspect of the problem for consideration is the numerical approximation of the compensator system in line with past work in [16,18]. For discretization of a fluid structure interactions see [20,21]. ...

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Boundary Stabilization for a Heat-Kelvin-Voigt Unstable Interaction Model, with Control and Partial Observation Localized at the Interface Only

... For example, in Manenti's [6] work, FSI simulation was used to simulate the effect of waves on floating offshore wind turbines. Several other FSI studies have also been done on the wind turbine [7][8][9][10][11]. Another example of FSI simulation implementation is the simulation of a parachute [12]. ...

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High-Fidelity 2-Way FSI Simulation of a Wind Turbine Using Fully Structured Multiblock Meshes in OpenFoam for Accurate Aero-Elastic Analysis

... Variational-hemivariational inequalities represent a special class of inequality problems which have both a convex and nonconvex structure. They have been intensively studied in the last decades as shown in [13,22,24,26,28,29,31] and the references therein. The penalty method we introduce in the current paper is new since, at the best of our knowledge, the penalty problems of (1) studied in the literature are in a form of variational inequality governed by a penalty operator and the main ingredients used there are based on pseudomonotonicity arguments. ...

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A new penalty method for elliptic variational inequalities

... Time delay systems represent one among the foremost in style categories of systems. Time delay, whether occurring in the system state, the control input, or the gauge, is often inescapable in practical systems and can be a source of instability and poor performance [5][6][7][8][9][10][11][12]. The future development of the system state of a time delay system consists not only of its current value, but also on its past values [13][14][15][16][17][18][19][20][21]. ...

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Stability Approach of a Fractional-Delayed Duffing Oscillator

... In addition, they proposed a numerical method based on a Newton type iteration and used it to solve coherent control problems. Friesecke et al [18] proposed a new class of cost functionals for the optimal control of quantum systems which result in controls with a sparse time-frequency structure. The theory and numerical solution of optimal control problems governed by a time-dependent Kohn-Sham model are investigated in [45,46]. ...

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Stability of the Transmission Schrödinger Equation with a Delay Term in the Boundary Feedback

... This includes for example denoising in image processing [14,25,44,45]. However, total variation regularization is also of great interest in terms of optimal control, see for instance [9,11,18,38], also in combination with integrality restrictions [39,40,41]. ...

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Dual Regularization and Outer Approximation of Optimal Control Problems in BV