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Wyświetlanie 1-15 z 22
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:
An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient
Autorzy:
Farahani, H. S.
Telabi, H. A.
Baghermenhaj, M.
Powiązania:
https://bibliotekanauki.pl/articles/229317.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
drilling systems
adaptive control
hyperbolic partial differential equations
wave equation
boundary control
Opis:
The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.
Źródło:
Archives of Control Sciences; 2017, 27, 1; 63-76
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Classical solutions of hyperbolic partial differential equations with implicit mixed derivative
Autorzy:
Marano, Salvatore
Powiązania:
https://bibliotekanauki.pl/articles/1312194.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
hyperbolic equation
implicit mixed derivative
classical solution
Opis:
Let f be a continuous function from $[0,a] × [0,β] × (ℝ^n)⁴$ into $ℝ^n$. Given $u₀,v₀ ∈ C⁰([0,β],ℝ^n)$, with f(0, x, ∫_0^x u₀(s)ds, ∫_0^x v₀(s)ds, u₀(x), v₀(x)) = v₀(x) for every x ∈ [0,β], consider the problem (P) { ∂²z/(∂t∂x) = f(t, x, z, ∂z/∂t, ∂z/∂x, ∂²z/(∂t∂x)),
$z(t,0) = ϑ_{ℝ^n}$, $z(0,x)=∫_0^x u₀(s)ds$, ∂²z(0,x)/(∂t∂x) = v₀(x). In this paper we prove that, under suitable assumptions, problem (P) has at least one classical solution that is local in the first variable and global in the other. As a consequence, we obtain a generalization of a result by P. Hartman and A. Wintner ([4], Theorem 1).
Źródło:
Annales Polonici Mathematici; 1991-1992, 56, 2; 163-178
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergence of optimal solutions in control problems for hyperbolic equations
Autorzy:
Migórski, S.
Powiązania:
https://bibliotekanauki.pl/articles/1311423.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
control problem
hyperbolic equation
G-convergence
Γ-convergence
Opis:
A sequence of optimal control problems for systems governed by linear hyperbolic equations with the nonhomogeneous Neumann boundary conditions is considered. The integral cost functionals and the differential operators in the equations depend on the parameter k. We deal with the limit behaviour, as k → ∞, of the sequence of optimal solutions using the notions of G- and Γ-convergences. The conditions under which this sequence converges to an optimal solution for the limit problem are given.
Źródło:
Annales Polonici Mathematici; 1995, 62, 2; 111-121
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Critical cases in neutral functional differential equations, arising from hydraulic engineering
Autorzy:
Răsvan, Vladimir
Powiązania:
https://bibliotekanauki.pl/articles/2216162.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
1D hyperbolic partial differential equations
neutral functional differential equation
difference operator
critical case
differential equations
Opis:
This paper starts from several applications described by initial/boundary value problems for 1D (time and one space variable) hyperbolic partial differential equations whose basic properties and stability of equilibria are studied throughout the same properties for certain associated neutral functional differential equations. It is a common fact that asymptotic stability for neutral functional differential equations is normally obtained under the assumption of asymptotic stability of the difference operator associated to the aforementioned neutral functional differential equations. However the physically meaningful applications presented in the paper have the associated difference operator(s) in critical cases (their stability is, generally speaking, non-asymptotic). Consequently the stability of the considered application models is either non-asymptotic or fragile (in a sense introduced in the paper). The models represent an overview gathered from various fields, processed here in order to emphasize the associated neutral functional differential equations which, consequently, are a challenge to the usual approaches. In the concluding part there are suggested possible ways to overcome these difficulties.
Źródło:
Opuscula Mathematica; 2022, 42, 4; 605-633
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact Neumann boundary controllability for second order hyperbolic equations
Autorzy:
Liu, Weijiu
Williams, Graham
Powiązania:
https://bibliotekanauki.pl/articles/966033.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Neumann boundary condition
HUM
exact controllability
second order hyperbolic equation
Opis:
Using HUM, we study the problem of exact controllability with Neumann boundary conditions for second order hyperbolic equations. We prove that these systems are exactly controllable for all initial states in $L^2({\mit\Omega})\times (H^1({\mit\Omega}))'$ and we derive estimates for the control time T.
Źródło:
Colloquium Mathematicum; 1998, 76, 1; 117-142
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence, uniqueness and estimates of classical solutions to some evolutionary system
Autorzy:
Sapa, L.
Powiązania:
https://bibliotekanauki.pl/articles/255005.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
hyperbolic wave equation
telegraph equation
system of nonlinear equations
existence
uniqueness and estimates of solutions
Hölder space
Opis:
The theorem of the local existence, uniqueness and estimates of solutions in Hölder spaces for some nonlinear differential evolutionary system with initial conditions is formulated and proved. This system is composed of one partial hyperbolic second-order equation and an ordinary subsystem with a parameter. In the proof of the theorem we use the Banach fixed-point theorem, the Arzeli-Ascola lemma and the integral form of the differential problem.
Źródło:
Opuscula Mathematica; 2015, 35, 6; 935-956
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extended models of sedimentation in coastal zone
Autorzy:
Selezov, I.
Powiązania:
https://bibliotekanauki.pl/articles/128092.pdf
Data publikacji:
2014
Wydawca:
Politechnika Poznańska. Instytut Mechaniki Stosowanej
Tematy:
sediment dynamics
hyperbolic equation
finite velocity
disturbance propagation
dynamika osadów dennych
równanie hiperboliczne
prędkość skończona
propagacja zaburzeń
Opis:
Construction of a generalized hyperbolic model of sediment dynamics predicting a sediment evolution on the bottom surface with a finite velocity is presented. The transport equation is extended with introducing a generalized operator of flux change and a generalized operator of gradient. Passing to the convenient model is a singular degeneration of extended model. In this case the results are obtained in the class of generalization solutions. Some expressive examples of constructions of hyperbolic models predicting a finite velocity of disturbance propagation are presented. This problem is developed starting from Maxwell (1861). His approach in the theory of electromagnetism and the kinetic theory of gases is commented. A brief review on propagation of heat and diffusive waves is presented. The similar problems in the theory of probability and diffusion waves are considered. In particular, it was shown on the microscopic level for metals that the conservation law can be violated.
Źródło:
Vibrations in Physical Systems; 2014, 26; 243-250
0860-6897
Pojawia się w:
Vibrations in Physical Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Investigation of non-Fourier thermal waves interaction in a solid material
Autorzy:
Lenarczyk, Marcin
Domański, Roman
Powiązania:
https://bibliotekanauki.pl/articles/240472.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
non-Fourier equation
heat waves
hyperbolic heat conduction
thermal wave interaction
fale cieplne
przewodzenie ciepła
Opis:
In this paper, effects of non-Fourier thermal wave interactions in a thin film have been investigated. The non-Fourier, hyperbolic heat conduction equation is solved, using finite difference method with an implicit scheme. Calculations have been carried out for three geometrical configurations with various film thicknesses. The boundary condition of a symmetrical temperature step-change on both sides has been used. Time history for the temperature distribution for each investigated case is presented. Processes of thermal wave propagation, temperature peak build-up and reverse wave front creation have been described. It has been shown that (i) significant temperature overshoot can appear in the film subjected to symmetric thermal load (which can be potentially dangerous for reallife application), and (ii) effect of temperature amplification decreases with increased film thickness.
Źródło:
Archives of Thermodynamics; 2019, 40, 1; 115-126
1231-0956
2083-6023
Pojawia się w:
Archives of Thermodynamics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Isometric immersions of the hyperbolic space $H^n(-1)$ into $H^{n+1}(-1)$
Autorzy:
Hu, Ze-Jun
Powiązania:
https://bibliotekanauki.pl/articles/1396048.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
isometric immersion
Monge-Ampère type equation
hyperbolic space
Opis:
We transform the problem of determining isometric immersions from $H^n(-1)$ into $H^{n+1}(-1)$ into that of solving equations of degenerate Monge-Ampère type on the unit ball $B^n(1)$. By presenting one family of special solutions to the equations, we obtain a great many noncongruent examples of such isometric immersions with or without umbilic set.
Źródło:
Colloquium Mathematicum; 1999, 79, 1; 17-23
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kinetic-induced moment systems for the Saint-Venant equations
Autorzy:
Gil Montoya, D. C.
Struckmeier, J.
Powiązania:
https://bibliotekanauki.pl/articles/1933941.pdf
Data publikacji:
2013
Wydawca:
Politechnika Gdańska
Tematy:
Saint-Venant equations
shallow water equations
Boltzmann equation
hyperbolic conservation laws
kinetic models
kinetic representations
relaxion systems
shock waves
rarefaction waves
Opis:
Based on the relation between kinetic Boltzmann-like transport equations and nonlinear hyperbolic conservation laws, we derive kinetic-induced moment systems for the spatially one-dimensional shallow water equations (the Saint-Venant equations). Using Chapman-Enskog-like asymptotic expansion techniques in terms of the relaxation parameter of the kinetic equation, the resulting moment systems are asymptotically closed without the need for an additional closure relation. Moreover, the new second order moment equation for the (asymptotically) third order system may act as a monitoring function to detect shock and rarefaction waves, which we confirm by a number of numerical experiments.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2013, 17, 1-2; 63-90
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lossless transmission lines terminated by crystal oscillator circuit
Autorzy:
Angelov, Vasil G.
Powiązania:
https://bibliotekanauki.pl/articles/1065397.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Fixed point theorem
Kirchhoff’s law
Lossless transmission line
Mixed problem for hyperbolic system
Neutral equation
Periodic solution
Opis:
The present paper deals with ТЕМ propagation of waves along lossless transmission lines terminated by a crystal oscillator circuit. The crystal oscillator circuit generates nonlinear boundary conditions derived by the Kirchhoff’s law. Then the mixed problem for the hyperbolic transmission line system to an initial value problem for neutral system on the boundary is reduced. The main purpose of the present paper is to show an existence-uniqueness of a periodic solution of the neutral system. This is achieved by introducing a suitable operator acting on a space of periodic functions. Its fixed point is a periodic solution of the neutral system. The advantages of the presented method on numerical example are demonstrated. The solution can be obtained by successive approximations.
Źródło:
World Scientific News; 2019, 132; 65-83
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear Choquard equations on hyperbolic space
Autorzy:
He, Haiyang
Powiązania:
https://bibliotekanauki.pl/articles/2216225.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
nonlinear Choquard equation
hyperbolic space
existence solutions
Hardy-Littlewood-Sobolev inequality
Opis:
In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation $ -\Delta_{ \mathbb{B}^{N} } u = \int_{\mathbb{B}^N} \frac{ |u(y)|^p } { | 2 \text{sin} \frac{ p(T_y(x)) }{ 2 } |^u } dV_y \cdot |u|^{p-2} u + \lambda u $ on the hyperbolic space BN, where ΔBN denotes the Laplace–Beltrami operator on BN, $ \text{sin} \text{h} \frac{\rho(T_y(x))}{2} = \frac{|T_y(x)|}{\sqrt{1-|T_y(x)|^2}} = \frac{ |x-y|}{\sqrt{(1-|x|^2)(1-|y|^2)} $ , λ is a real parameter, 0 < μ < N, 1 < p ≤ 2∗μ,N ≥ 3 and [formula] is the critical exponent in the sense of the Hardy–Littlewood–Sobolev inequality.
Źródło:
Opuscula Mathematica; 2022, 42, 5; 691-708
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical scheme methods for solving nonlinear pseudo-hyperbolic partial differential equations
Autorzy:
Abdulazeez, Sadeq Taha
Modanli, Mahmut
Husien, Ahmad Muhamad
Powiązania:
https://bibliotekanauki.pl/articles/2202054.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
nonlinear pseudo-hyperbolic partial differential equation
homotopy analysis method
variational iteration method
approximate solution
nieliniowe pseudohiperboliczne równanie różniczkowe cząstkowe
homotopijna metoda analizy
metoda iteracji wariacyjnych
rozwiązanie przybliżone
Opis:
The numerical solutions to the nonlinear pseudo-hyperbolic partial differentia equation with nonlocal conditions are presented in this study. This equation is solved using the homotopy analysis technique (HAM) and the variational iteration method (VIM). Both strategies are compared and contrasted in terms of approximate and accurate solutions. The results show that the HAM technique is more appropriate, effective, and close to the exact solution than the VIM method. Finally, the graphical representations of the obtained results are given.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 4; 5--15
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a finding the coefficient of one nonlinear wave equation in the mixed problem
Autorzy:
Safarova, Zimrud R.
Powiązania:
https://bibliotekanauki.pl/articles/229359.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
hyperbolic equation
nonlinear wave equation
optimal control problem
necessary condition
Opis:
The paper is devoted to the finding of the coefficient of one nonlinear wave equation in the mixed problem. The considered problem is reduced to the optimal control problem with proper functional. Differentiability of functional is proved and the necessary optimality conditions are derived in the form of the variational inequality. Existence of the optimal control is proved.
Źródło:
Archives of Control Sciences; 2020, 30, 2; 199-212
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 22

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