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Control and Cybernetics
EN Various controllability types are demonstrated for a circular membrane with rotationally symmetric initial data and boundary control depending on time only. We prove that the set of initial states, which can be steered to rest in the critical time interval (equal to the diameter of the membrane) by [...]
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Control and Cybernetics
EN In a previous work we improved some earlier results of Imanuvilov, Li and Zhang, and of Zuazua, on the boundary exact controllability of semilinear wave equations by weakening the growth assumptions on the nonlinearity. Answering a question of Zuazua we give a still weaker, essentially optimal condi[...]
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Hydroacoustics
2003 Vol. 6 137--142
EN 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 ul[...]
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Computational Methods in Science and Technology
EN The paper presents a specific technique to generate the Trefftz functions for the two-dimensional wave equation. The obtained functions are used to determine approximate solutions of some tested problems. The accuracy of the method is discussed.
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Poznan University of Technology Academic Journals. Electrical Engineering
2012 No. 69 161--168
EN In the paper a difference interval method for solving the wave equation together the initial-boundary value problems is presented. Using an interval method together floating-point interval arithmetic guarantee, that obtained interval solutions contain all numerical errors. Additionally, each exact s[...]
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Archives of Control Sciences
EN 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 [...]
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Control and Cybernetics
EN We derive global in time a priori bounds on higher-level energy norms of strong solutions to a semilinear wave equation: in particular, we prove that despite the influence of a nonlinear source, the evolution of a smooth initial state is globally bounded in the strong topology ∼ H2 x H1. And the bou[...]
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International Journal of Applied Mathematics and Computer Science
EN Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elements of order k and show how it is possible to automatically generate the mass and stiffness matrices of any or[...]
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Engineering Transactions
EN The paper demonstrates a new technique of obtaining the approximate solution of the two- and threedimensional elasticity problems. The system of equations of elasticity can be converted to the system of wave equation. In this case, as solving functions (Trefftz functions), the so-called wave polynom[...]
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Computer Assisted Mechanics and Engineering Sciences
EN The paper demonstrates a specific power series expansion technique used to obtain the approximate solution of the two-dimensional wave equation in some unusual cases. The solution for inhomogeneous wave equation, for more complicated shape geometry of the body, discrete boundary conditions and a mem[...]
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Journal of Applied Mathematics and Computational Mechanics
2014 Vol. 13, nr 3 129--140
EN The paper presents a method of solving two-dimensional wave equations which describe vibrations of the membrane with variable thickness and with damping. The differential operator is decomposed into two parts. The first one describes vibrations of the membrane with constant thickness without damping[...]
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Bulletin of the Polish Academy of Sciences. Mathematics
EN The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of R^n. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space H[...]^R^n) x L[...](R^n). Asymptotic compactness of this semigroup and the e[...]
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Eksploatacja i Niezawodność
2009 nr 1 39-45
PL Praca przedstawia analizę dynamiki stanu pracy górniczego urządzenia wyciągowego w warunkach hamowania bezpieczeństwa. Proces hamowania bezpieczeństwa przedstawiono za pomocą modelu mechanicznego z uwzględnieniem liniowo narastającej wartości siły hamowania zastosowanej do koła pędnego. Na podstawie[...]
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International Journal of Applied Mathematics and Computer Science
EN We consider a linear damped wave equation defined on a two-dimensional domain [...], with a dissipative term localized in a subset [...]. We address the shape design problem which consists in optimizing the shape of [...] in order to minimize the energy of the system at a given time T. By introducin[...]
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Journal of Applied Analysis
EN We give a meaning to the nonlinear characteristic Cauchy problem for the wave equation in base form by replacing it by a family of non-characteristic ones. This leads to a well-formulated problem in an appropriate algebra of generalized functions. We prove existence of a solution and we precise how [...]
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Acta of Bioengineering and Biomechanics
EN The paper deals with the method of modelling of blood pulsatory flow in the vessels of circulatory system. The method is based upon the solution of wave equation applied in the theory of four-pole. In a graphic presentation of a vessel of distributed parameters, a model of bond graphs with new eleme[...]
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Journal of Technical Physics
EN In this paper we study the weakly nonlinear interaction of two waves whose propagation is governed by hyperbolic systems of balance laws. The method used here makes use of nonlinear phase variables and consists in a perturbation analysis. It is applied to an Eulerian gas and to a gas described by ex[...]
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Control and Cybernetics
EN The paper provides a short introduction into the theory of boundary exact controllability and uniform stabilization of linear distributed systems, based on the multiplier method.
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Przegląd Elektrotechniczny
2017 R. 93, nr 3 171--174
PL W niniejszym artykule opisujemy zbudowany model numeryczny MES rozwiązujący zespolone, wektorowe równanie falowe Helmholtza. Pozwala on na modelowanie zjawisk propagacji fal elektromagnetycznych wysokich częstotliwości. Zaprezentowany model może zostać wykorzystany w systemie poszukującym optymalneg[...]
EN This paper describes a numerical FEM model for solving the complex-valued, vector Helmholtz wave equation. The model describes phenomena of electromagnetic wave propagation for high frequencies. The presented model can be used in a larger system seeking an efficient design parameters of electromagne[...]
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Biuletyn Wojskowej Akademii Technicznej
PL Skonstruowano w postaci zamkniętych algebraicznych wzorów rozwiązanie zagadnienia Darboux dla nieliniowego równania falowego, opisującego jednowymiarowy płaski ruch produktów detonacji w problemie przeciwbieżnego napędzania sztywnych ciał za pomocą skondensowanego materiału wybuchowego. Wyprowadzone[...]
EN In the from of closed algebraic relations are constructed solution of the Darboux problem for nonlinear wave equation describing the one-dimensional flat motion of explosion products in the problem of the opposite acceleration of the rigid bodies by condensed explosives. The derived relations one ca[...]
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