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Wyszukujesz frazę "partial differential equation" wg kryterium: Temat

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    Wyświetlanie 1-6 z 6
    Tytuł:
    Feedback design of differential equations of reconstruction for second-order distributed parameter systems
    Autorzy:
    Maksimov, V. I.
    Mordukhovich, B. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/330817.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    partial differential equation
    equations of reconstruction
    distributed parameter system
    równanie różniczkowe cząstkowe
    układ o parametrach rozłożonych
    równanie drugiego rzędu
    Opis:
    The paper aims at studying a class of second-order partial differential equations subject to uncertainty involving unknown inputs for which no probabilistic information is available. Developing an approach of feedback control with a model, we derive an efficient reconstruction procedure and thereby design differential equations of reconstruction. A characteristic feature of the obtained equations is that their inputs formed by the feedback control principle constructively approximate unknown inputs of the given second-order distributed parameter system.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 467-475
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework
    Autorzy:
    Chaturantabut, Saifon
    Powiązania:
    https://bibliotekanauki.pl/articles/1838159.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    model order reduction
    ordinary differential equation
    partial differential equation
    proper orthogonal decomposition
    discrete empirical interpolation method
    redukcja rzędu modelu
    równanie różniczkowe zwyczajne
    równanie różniczkowe cząstkowe
    rozkład ortogonalny
    Opis:
    This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 4; 615-628
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Travelling waves for low-grade glioma growth and response to a chemotherapy model
    Autorzy:
    Bartłomiejczyk, Agnieszka
    Bodnar, Marek
    Bogdańska, Magdalena U.
    Piotrowska, Monika J.
    Powiązania:
    https://bibliotekanauki.pl/articles/24202933.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    low grade glioma
    generalized model
    partial differential equation
    wave solution
    chemotherapy model
    glejak
    model uogólniony
    równanie różniczkowe cząstkowe
    rozwiązanie falowe
    model chemioterapii
    Opis:
    Low-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the basic mathematical properties of the model, we study the possibility of the existence of travelling wave solutions in the framework of Fenichel’s invariant manifold theory. The estimates of the minimum speeds of the travelling wave solutions are provided. The obtained analytical results are illustrated by numerical simulations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2023, 33, 4; 569--581
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A general transfer function representation for a class of hyperbolic distributed parameter systems
    Autorzy:
    Bartecki, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/330308.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    distributed parameter system
    hyperbolic system
    partial differential equation
    transfer function
    heat exchanger
    układ o parametrach rozłożonych
    system hiperboliczny
    równanie różniczkowe cząstkowe
    funkcja przeniesienia
    wymiennik ciepła
    Opis:
    Results of transfer function analysis for a class of distributed parameter systems described by dissipative hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of two boundary inputs, the closed-form expressions for the individual elements of the 2×2 transfer function matrix are derived both in the exponential and in the hyperbolic form, based on the decoupled canonical representation of the system. Some important properties of the transfer functions considered are pointed out based on the existing results of semigroup theory. The influence of the location of the boundary inputs on the transfer function representation is demonstrated. The pole-zero as well as frequency response analyses are also performed. The discussion is illustrated with a practical example of a shell and tube heat exchanger operating in parallel- and countercurrent-flow modes.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2013, 23, 2; 291-307
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion
    Autorzy:
    Tagade, P. M.
    Choi, H. L.
    Powiązania:
    https://bibliotekanauki.pl/articles/330516.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    Bayesian framework
    stochastic partial differential equation
    Karhunen–Loève expansion
    generalized polynomial chaos
    dynamically biorthogonal field equations
    ramy Bayesa
    stochastyczne równanie różniczkowe
    przekształcenie Karhunena-Loeve'a
    chaos wielomianowy
    Opis:
    This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen–Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 2; 229-243
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis
    Autorzy:
    Cherniha, R.
    Stachowska-Piętka, J.
    Waniewski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/907934.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    fluid transport
    transport in peritoneal dialysis
    nonlinear partial differential equations
    ordinary differential equation
    steady-state solution
    transport płynu
    dializa otrzewnowa
    nieliniowe równanie różniczkowe
    równanie różniczkowe zwyczajne
    Opis:
    A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a three-component nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations as well as hydrostatic pressure. The model is developed in one spatial dimension approximation, and a governing equation for each of the variables is derived from physical principles. Under some assumptions the model can be simplified to obtain exact formulae for spatially non-uniform steady-state solutions. As a result, the exact formulae for fluid fluxes from blood to the tissue and across the tissue are constructed, together with two linear autonomous ODEs for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 837-851
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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