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Wyświetlanie 1-15 z 18
Tytuł:
Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces
Autorzy:
Brandolini, Luca
Colzani, Leonardo
Powiązania:
https://bibliotekanauki.pl/articles/966988.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
rearrangement invariant Banach function spaces
Schrödinger and wave equations
Fourier transform
multipliers
Źródło:
Colloquium Mathematicum; 1996, 71, 2; 273-286
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact boundary controllability of coupled hyperbolic equations
Autorzy:
Avdonin, S.
Choque Rivero, A.
de Teresa, L.
Powiązania:
https://bibliotekanauki.pl/articles/330237.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
coupled wave equations
controllability
Riesz bases
moment problem
równanie falowe
sterowalność
bazy Riesza
Opis:
We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent results on the Riesz basis property of exponential divided differences.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2013, 23, 4; 701-710
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient optimality conditions for multivariable control problems
Autorzy:
Nowakowski, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/729408.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
sufficient optimality condition
wave equations
parbolic equation
elliptic equation
Dirichlet boundary controls
dual dynamic programming
Opis:
We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 1; 135-150
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms
Autorzy:
Barbu, V.
Lasiecka, I.
Rammaha, A.
Powiązania:
https://bibliotekanauki.pl/articles/970548.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równanie falowe
rozwiązania słabe
wave equations
damping and source terms
weak solutions
subdifferential
blow-up of solutions
energy estimates
Opis:
In this article we focus on the global well-posedness of the differential equation u [...] in Omega x(O, T), where j' denotes the derivative of a C1 convex and real valued function j. The interaction between degenerate damping and a source term constitutes the main challenge of the problem. Problems with non-degenerate damping (k = 0) have been studied in the literature (Georgiev and Todorova, 1994; Levine and Serrin, 1997; Vitillaro, 2003). Thus the degeneracy of monotonicity is the main novelty of this work. Depending on the level of interaction between the source and the damping we characterize the domain of the parameters p, m, k, n (see below) for which one obt ains existence, regularity or finite time blow up of solutions. More specifically, when p [is less than or equal to] m + k global existence of generalized solutions in H1 x L2 is proved. For p > m + k, solutions blow up in a finite time. Higher energy solutions are studied as well. For H2 x H1 initial data we obtain both local and global solutions with the same regularity. Higher energy solutions are also proved to be unique.
Źródło:
Control and Cybernetics; 2005, 34, 3; 665-687
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear equations of acoustics - numerical solutions and their visualization
Autorzy:
Wójcik, J.
Lewin, P. A.
Nowicki, A.
Filipczyński, L.
Kujawska, T.
Radulescu, E.
Powiązania:
https://bibliotekanauki.pl/articles/331971.pdf
Data publikacji:
2003
Wydawca:
Polskie Towarzystwo Akustyczne
Tematy:
acoustics
nonlinear equations
wave equation
Opis:
The novel effective numeric solver of the nonlinear scalar wave equation describing the acoustic wave propagation in the attenuating media was derived. The solver was developed for the PC environment. The standard computation data include al! stationary and dynamic characteristics of the radiated ultrasonic pressure field, especially its 4D (space/time) visualization. The results obtained with the solver can be used as the supporting tools (tool) in designing and developments of the multielement linear and phase array transducers applied in ultrasonography.
Źródło:
Hydroacoustics; 2003, 6; 137-142
1642-1817
Pojawia się w:
Hydroacoustics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical Method for Modeling of Acoustic Waves Propagation
Autorzy:
Dykas, S.
Wróblewski, W.
Rulik, S.
Chmielniak, T.
Powiązania:
https://bibliotekanauki.pl/articles/177994.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
acoustic wave
fluctuations
aerodynamic noise
Euler equations
Opis:
In this paper, numerical results of modeling of acoustic waves propagation are presented. For calculation of the acoustic fluctuations, a solution of the full non-linear Euler equation is used. The Euler equations are solved with the use of a numerical scheme of third-order accuracy in space and time. The paper shows a validation process of the described method. This method is suitable also for an aerodynamic noise assessment on the basis of unsteady mean flow field data obtained from a CFD calculations. In such case this method is called a hybrid CFD/CAA method. The proposed method is numerically decoupled with CFD solution, therefore the information about the mean unsteady flow field can be obtained using an arbitrary CFD method (solver). The accuracy of the acoustic field assessment depends on the quality of the CFD solutions. This decomposition reduces considerably the computational cost in comparison with direct noise calculations. The presented Euler acoustic postprocessor (EAP) has been used for modeling of the acoustic waves propagation in a cavity and in the flow field around a cylinder and an aerodynamic profile.
Źródło:
Archives of Acoustics; 2010, 35, 1; 35-48
0137-5075
Pojawia się w:
Archives of Acoustics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Studies of Nonlinear Sound Dynamics in Fluids Based on the Caloric Equation of State
Autorzy:
Perelomova, A.
Wojda, P.
Powiązania:
https://bibliotekanauki.pl/articles/177850.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
nonlinear acoustics
parameters of nonlinearity
equations of state
Riemann wave
Opis:
The sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting of boiling water and its vapor under different temperatures, are evaluated as functions of mass concentration of the vapor. The relations analogous to that in the Riemann wave in an ideal gas are obtained in a fluid obeying an arbitrary equation of state. An example concerns the van der Waals gases. An excess pressure in the reflected wave, which appears when standard or nonlinear absorption in a fluid takes place, is evaluated in an arbitrary fluid.
Źródło:
Archives of Acoustics; 2010, 35, 4; 619-633
0137-5075
Pojawia się w:
Archives of Acoustics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A finite element method for extended KdV equations
Autorzy:
Karczewska, A.
Rozmej, P.
Szczeciński, M.
Boguniewicz, B.
Powiązania:
https://bibliotekanauki.pl/articles/330630.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
shallow water wave problem
nonlinear equations
second order KdV equations
finite element method
Petrov–Galerkin method
Opis:
The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov–Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2016, 26, 3; 555-567
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Pseudo-differential equations and conical potentials: 2-dimensional case
Autorzy:
Vasilyev, Vladimir B.
Powiązania:
https://bibliotekanauki.pl/articles/255700.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
pseudo-differential equation
wave factorization
Dirichlet problem
system of linear integral equations
Opis:
We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.
Źródło:
Opuscula Mathematica; 2019, 39, 1; 109-124
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Towards a Framework for Continuous and Discrete Multidimensional Systems
Autorzy:
Rabenstein, R.
Trautmann, L.
Powiązania:
https://bibliotekanauki.pl/articles/908258.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
automatyka
robotyka
multidimensional systems
partial differential equations
transfer functions
wave digital models
Opis:
Continuous multidimensional systems described by partial differential equations can be represented by discrete systems in a number of ways. However, the relations between the various forms of continuous, semi-continuous, and discrete multidimensional systems do not fit into an established framework like in the case of one-dimensional systems. This paper contributes to the development of such a framework in the case of multidimensional systems. First, different forms of partial differential equations of physics-based systems are presented. Secondly, it is shown how the different forms of continuous multidimensional systems lead to certain discrete models in current use (finite-difference models, multidimensional wave digital filters, transfer function models). The links between these discrete models are established on the basis of the respective continuous descriptions. The presentation is based on three examples of physical systems (heat flow, transmission of electrical signals, acoustic wave propagation).
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 1; 73-85
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear Interaction of Modes in a Planar Flow of a Gas with Viscous and Thermal Attenuation
Autorzy:
Perelomova, Anna
Powiązania:
https://bibliotekanauki.pl/articles/177137.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
nonlinear wave theory
nonlinear acoustics
coupling dynamic equations
Burgers equation
diffusion equation
Opis:
The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differentia form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.
Źródło:
Archives of Acoustics; 2019, 44, 3; 551-559
0137-5075
Pojawia się w:
Archives of Acoustics
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:
Modelling of Flood Wave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation
Autorzy:
Gąsiorowski, D.
Powiązania:
https://bibliotekanauki.pl/articles/241192.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
diffusive wave equation
shallow water equations
overland flow
floodplain inundation
finite element method
Opis:
A full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of a moving wet-dry front, which lead to instability in numerical solutions. To overcome these difficulties, a simplified model in the form of a non-linear diffusive wave equation (DWE) can be used. The diffusive wave approach requires numerical algorithms that are much simpler, and consequently, the computational process is more effective than in the case of the SWE. In this paper, the numerical solution of the one-dimensional DWE based on the modified finite element method is verified in terms of accuracy. The resulting solutions of the DWE are compared with the corresponding benchmark solution of the one-dimensional SWE obtained by means of the finite volume methods. The results of numerical experiments show that the algorithm applied is capable of reproducing the reference solution with satisfactory accuracy even for a rapidly varied wave over a dry bottom.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2014, 61, 3-4; 111--125
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of the dike-break problem using finite volume method and splitting technique
Autorzy:
Gąsiorowski, D.
Powiązania:
https://bibliotekanauki.pl/articles/1934027.pdf
Data publikacji:
2011
Wydawca:
Politechnika Gdańska
Tematy:
finite volume method
shallow water equations
approximate Riemann solver
dambreak
dike-break
wave-propagation method
Opis:
In this paper, an approach using the finite volume method (FVM) for the solution of two-dimensional shallow water equations is described. Such equations are frequently used to simulate dam-break and dike-break induced flows. The applied numerical algorithm of the FVM is based on a wave-propagation algorithm, which ensures a stable solution and, simultaneously, minimizes numerical errors. Dimensional decomposition according to the coordinate directions was used to split two-dimensional shallow water equations into one-dimensional equations. Additionally, splitting was also applied with respect to the physical processes. The applied dimensional and physical splitting, together with the wave-propagation algorithm led to an effective algorithm and ensured proper incorporation of source terms into the scheme of the finite volume method. A detailed description of an approximation for numerical fluxes and source terms is presented. The obtained numerical results are compared with analytical solutions, laboratory experiments and other results available in the literature.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2011, 15, 3-4; 251-270
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
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
Wyświetlanie 1-15 z 18

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