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    Wyświetlanie 1-8 z 8
    Tytuł:
    Rigorous Numerics for PDEs with Indefinite Tail: Existence of a Periodic Solution of the Boussinesq Equation with Time-dependent Forcing
    Autorzy:
    Czechowski, Aleksander
    Zgliczyński, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/1373703.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
    Tematy:
    Boussinesq equation
    ill-posed PDEs
    periodic solutions
    isolating segments
    Opis:
    We consider the Boussinesq PDE perturbed by a time-dependent forcing. Even though there is no smoothing effect for arbitrary smooth initial data, we are able to apply the method of self-consistent bounds to deduce the existence of smooth classical periodic solutions in the vicinity of 0. The proof is non-perturbative and relies on construction of periodic isolating segments in the Galerkin projections.
    Źródło:
    Schedae Informaticae; 2015, 24; 143-158
    0860-0295
    2083-8476
    Pojawia się w:
    Schedae Informaticae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities
    Autorzy:
    Zuazua, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/206681.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    controllability
    nolinear PDEs of parabolic type
    systems governed by PDFs
    Opis:
    We consider the semilinear heat equation involving gradient terms in a bounded domain of [R^n]. It is assumed that the non-linearity is globally Lipschitz. We prove that the system is approximately controllable when t1e control acts on a bounded subset of the domain. The proof uses a variant of a classical fixed point method and is a simpler alternative to the earlier proof existing in the literature by means of the penalization of an optimal control problem. We also prove that the contool may be built so that, in addition to the approximate controllability requirement, it ensures that the state reaches exactly a finite number of constraints.
    Źródło:
    Control and Cybernetics; 1999, 28, 3; 665-683
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some constructive applications of $Λ^{2}$-representations to integration of PDEs
    Autorzy:
    Popov, A.
    Zadadaev, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1207978.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    discrete net
    $Λ^{2}$-representations of PDEs
    Lobachevsky (hyperbolic) geometry
    pseudospherical metric
    Opis:
    Two new applications of $Λ^{2}$-representations of PDEs are presented: 1. Geometric algorithms for numerical integration of PDEs by constructing planimetric discrete nets on the Lobachevsky plane $Λ^{2}$. 2. Employing $Λ^{2}$-representations for the spectral-evolutionary problem for nonlinear PDEs within the inverse scattering problem method.
    Źródło:
    Annales Polonici Mathematici; 2000, 74, 1; 261-274
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundary layer homogenization for periodic oscillating boundaries
    Autorzy:
    Habbal, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/205717.pdf
    Data publikacji:
    2001
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    okresowe wahania graniczne
    równanie różniczkowe cząstkowe
    warstwa graniczna
    boundary layer
    PDEs
    periodic oscillating boundaries
    Opis:
    The paper is devoted to the study of the boundary layer behaviour of solutions to partial differential equations occurring in domains with periodic oscillating boundaries, the frequency and the amplitude of the oscillations being the same. First, the transport method, a classical one from the optimal design theory, is used in order to state the problem in a fixed domain ; then, an adapted two-scale boundary layer convergence is developed. Apart from this new hybrid approach, the main difference with related works is consideration of a bounded unit-cell, yielding a simple functional framework. Convergence, as well as a homogenized equation for the first order boundary layer term are given, and a first order corrector result is proved. This a priori boundingg is very well suited to problems of control, and to numerical implementation considerations. The difficulty in obtaining higher order correctors due to the bounding of the unit-cell is finally discussed.
    Źródło:
    Control and Cybernetics; 2001, 30, 3; 279-301
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Applications of PDES inpainting to magnetic particle imaging and corneal topography
    Autorzy:
    Andrisani, Andrea
    Mininni, Rosa Maria
    Mazzia, Francesca
    Settanni, Giuseppina
    Iurino, Alessandro
    Tangaro, Sabina
    Tateo, Andrea
    Bellotti, Roberto
    Powiązania:
    https://bibliotekanauki.pl/articles/255026.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    PDEs inpainting
    medical imaging
    magnetic particle imaging
    radial curvature image
    anterior surface of a cornea
    Opis:
    In this work we propose a novel application ol Partial Differential Equations (PDEs) inpainting techniques to two medical contexts. The first one concerning recovering of concentration maps for superparamagnetic nanoparticles, used as tracers in the framework of Magnetic Particle Imaging. The analysis is carried out by two set of simulations, with and without adding a source of noise, to show that the inpainted images preserve the main properties of the original ones. The second medical application is related to recovering data of corneal elevation maps in ophthalmology. A new procedure consisting in applying the PDEs inpainting techniques to the radial curvature image is proposed. The images of the anterior corneal surface are properly recovered to obtain an approximation error of the required precision. We compare inpainting methods based on second, third and fourth-order PDEs with standard approximation and interpolation techniques.
    Źródło:
    Opuscula Mathematica; 2019, 39, 4; 453-482
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimal control problems without terminal constraints: The turnpike property with interior decay
    Autorzy:
    Gugat, Martin
    Lazar, Martin
    Powiązania:
    https://bibliotekanauki.pl/articles/24200685.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    optimal control
    turnpike property
    system with hyperbolic PDEs
    interior decay
    sterowanie optymalne
    układ hiperboliczny
    rozkład wewnętrzny
    Opis:
    We show a turnpike result for problems of optimal control with possibly nonlinear systems as well as pointwise-in-time state and control constraints. The objective functional is of integral type and contains a tracking term which penalizes the distance to a desired steady state. In the optimal control problem, only the initial state is prescribed. We assume that a cheap control condition holds that yields a bound for the optimal value of our optimal control problem in terms of the initial data. We show that the solutions to the optimal control problems on the time intervals [0, T] have a turnpike structure in the following sense: For large T the contribution to the objective functional that comes from the subinterval [T/2, T], i.e., from the second half of the time interval [0, T], is at most of the order 1/T. More generally, the result holds for subintervals of the form [r T,T], where r ∈ (0, 1/2) is a real number. Using this result inductively implies that the decay of the integral on such a subinterval in the objective function is faster than the reciprocal value of a power series in T with positive coefficients. Accordingly, the contribution to the objective value from the final part of the time interval decays rapidly with a growing time horizon. At the end of the paper we present examples for optimal control problems where our results are applicable.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2023, 33, 3; 429--438
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Exact controllability of a string to rest with a moving boundary
    Autorzy:
    Gugat, Martin
    Powiązania:
    https://bibliotekanauki.pl/articles/970107.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    pde constrained optimization
    optimal control of pdes
    optimal boundary control
    wave equation
    analytic solution
    exact controllability
    moving boundaries
    mining elevator
    Opis:
    We consider the problem of steering a finite string to the zero state in finite time from a given initial state by controlling the state at one boundary point while the other boundary point moves. As a possible application we have in mind the optimal control of a mining elevator, where the length of the string changes during the transportation process. During the transportation process, oscillations of the elevator-cable can occur that can be damped in this way. We present an exact controllability result for Dirichlet boundary control at the fixed end of the string that states that there exist exact controls for which the oscillations vanish after finite time. For the result we assume that the movements are Lipschitz continuous with a Lipschitz constant, whose absolute value is smaller than the wave speed. In the result, we present the minimal time, for which exact controllability holds, this time depending on the movement of the boundary point. Our results are based upon travelling wave solutions. We present a representation of the set of successful controls that steer the system to rest after finite time as the solution set of two point-wise equalities. This allows for a transformation of the optimal control problem to a form where no partial differential equation appears. This representation enables interesting insights into the structure of the successful controls. For example, exact bang-bang controls can only exist if the initial state is a simple function and the initial velocity is zero.
    Źródło:
    Control and Cybernetics; 2019, 48, 1; 69-87
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Inverse shape optimization problems and application to airfoils
    Autorzy:
    Desideri, J.-A.
    Zolesio, J.-P.
    Powiązania:
    https://bibliotekanauki.pl/articles/970144.pdf
    Data publikacji:
    2005
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie różniczkowe cząstkowe
    metody obliczeniowe
    optymalizacja kształtu
    rachunek wariacyjny
    Partial-Differential Equations (PDEs)
    computational methods
    shape optimization
    calculus of variations
    Opis:
    We consider a set of parameterized planar arcs (x(t), y(t)) (0 1. We first prove the strict convexity of the functional for alpha > 2. Under the less stringent condition alpha > 1, we derive the stationarity condition and the formal expression for the Hessian, and prove that if a point exists at which the functional is stationary w.r.t. variations in y = y(t), for fixed x = x(t), then it is unique and realizes a global minimum; the functional is then unimodal. We also observe that the stationarity condition (Euler-Lagrange quation) is an integral-differential equation depending only on the arc shape and not on the parameterization per se, which gives the variational problem a certain intrinsic character. Then, we solve the inverse problem: given an admissible parameterized arc, we construct a smooth weighting function omega(t) for which the stationarity condition is satisfied, thus making the functional unimodal, and derive certain asymptotics. A numerical example pertaining to optimum-shape design in aerodynamics is computed for illustration.
    Źródło:
    Control and Cybernetics; 2005, 34, 1; 165-202
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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