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    Wyświetlanie 1-12 z 12
    Tytuł:
    Modeling of the finite amplitude plane wave propagation in non-dissipative medium
    Autorzy:
    Baranowska, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/331517.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Akustyczne
    Tematy:
    amplitude plane wave
    Burgers equation
    mathematical model
    Opis:
    The paper presents results of theoretical analysis of the finite amplitude plane wave propagation problem. The case of harmonic plane wave propagation in non-dissipative medium was considered. The mathematical model and some results of numerical investigations are presented. The mathematical model was built on the basis of one-dimensional continuity equation, equation of motion in differential form and state equation. The finite difference method was applied to solve the problem numerically. The pressure changes and harmonic pressure amplitude changes were analysed. The results of computer calculations were compared with solution of the Burgers equation.
    Źródło:
    Hydroacoustics; 2008, 11; 11-18
    1642-1817
    Pojawia się w:
    Hydroacoustics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotics for multifractal conservation laws
    Autorzy:
    Biler, Piotr
    Karch, Grzegorz
    Woyczynski, Wojbor
    Powiązania:
    https://bibliotekanauki.pl/articles/1216945.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    generalized Burgers equation
    fractal diffusion
    asymptotics of solutions
    Opis:
    We study asymptotic behavior of solutions to multifractal Burgers-type equation $u_t + f(u)_x = Au$, where the operator A is a linear combination of fractional powers of the second derivative $-∂^2/ ∂ x^2$ and f is a polynomial nonlinearity. Such equations appear in continuum mechanics as models with fractal diffusion. The results include decay rates of the $L^p$-norms, 1 ≤ p ≤ ∞, of solutions as time tends to infinity, as well as determination of two successive terms of the asymptotic expansion of solutions.
    Źródło:
    Studia Mathematica; 1999, 135, 3; 231-252
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Global existence for strong solutions of viscous Burgers equation. (1) The bounded case
    Autorzy:
    Unterberger, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/206077.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    viscous Burgers equation
    conservation laws
    maximum principle
    Schauder estimates
    Opis:
    We prove that the viscous Burgers equation (∂t−∆)u(t, x)+( u •∇)u(t, x) = g(t, x), (t, x) ∈ R+ × Rd (d ≥ 1) has a globally defined smooth solution in all dimensions provided the initial condition and the forcing term g are smooth and bounded together with their derivatives. Such solutions may have infinite energy. The proofdoes not rely on energy estimates, but on a combinationof the maximumprinciple and quantitative Schauder estimates. We obtain precise bounds on the sup norm of the solution and its derivatives, making it plain that there is no exponential increase in time. In particular, these bounds are time-independent if g is zero. To get a classical solution, it suffices to assume that the initial condition and the forcing term have bounded derivatives up to order two.
    Źródło:
    Control and Cybernetics; 2017, 46, 2; 109-136
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotic profiles for a class of perturbed burgers equations in one space dimension
    Autorzy:
    Dkhil, F.
    Hamza, M. A.
    Mannoubi, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/254933.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Burgers equation
    self-similar variables
    asymptotic behavior
    self-similar solutions
    Opis:
    In this article we consider the Burgers equation with some class of perturbations in one space dimension. Using various energy lunctionals in appropriate weighted Sobolev spaces rewritten in the variables [formula] and log τ, we prove that the large time behavior of solutions is given by the sell-similar solutions ol the associated Burgers equation.
    Źródło:
    Opuscula Mathematica; 2018, 38, 1; 41-80
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    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:
    Computer Assisted Proofs in Dissipative Partial Differential Equations
    Autorzy:
    Cyranka, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/115445.pdf
    Data publikacji:
    2012
    Wydawca:
    Fundacja na Rzecz Młodych Naukowców
    Tematy:
    rigorous numerics
    Lohner algorithm
    viscous Burgers equation
    interval arithmetic
    dissipative partial differential equations
    Opis:
    The goal of this paper is to present a brief survey of our research that has focused on studying the dynamics of dissipative partial differential equations by performing computer as sisted proofs. We provide a description of the main ideas behind the computer assisted proofs that we have performed, along with related topics. The emphasis is given to the case of the vis cous Burgers equation with constant forcing, for which the existence of globally attracting fixed points has been established. To achieve this goal, we used a combination of analytical results with computer assistance.
    Źródło:
    Challenges of Modern Technology; 2012, 3, 3; 3-6
    2082-2863
    2353-4419
    Pojawia się w:
    Challenges of Modern Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Rigorous Integration of Burgers Equation
    Autorzy:
    Cyranka, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/115776.pdf
    Data publikacji:
    2011
    Wydawca:
    Fundacja na Rzecz Młodych Naukowców
    Tematy:
    rigorous numerics
    Lohner algorithm
    Burgers equation
    rigorous integration
    dissipative partial differential equations
    interval arithmetics
    Opis:
    This paper presents techniques that allows to rigorously integrate dissipative partial differential equations. A full case study of an application to the Burgers equation on the line with periodic boundary conditions is presented.
    Źródło:
    Challenges of Modern Technology; 2011, 2, 3; 3-7
    2082-2863
    2353-4419
    Pojawia się w:
    Challenges of Modern Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Reduced order controllers for Burgers equation with a nonlinear observer
    Autorzy:
    Atwell, J. A.
    Borggaard, J. T.
    King, B. B.
    Powiązania:
    https://bibliotekanauki.pl/articles/908128.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie Burgersa
    obserwatory nieliniowe
    Burgers' equation
    reduced order controllers
    proper orthogonal decomposition
    minmax control design
    stabilized finite elements
    Opis:
    A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal decomposition (POD). However, the test problem was the two-dimensional heat equation, a problem in which the physics dominates the system in such a way that controller efficacy is difficult to generalize. Here, we additionally incorporate a nonlinear observer by including the nonlinear terms of the state equation in the differential equation for the compensator.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1311-1330
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear boundary control of coupled Burgers equations
    Autorzy:
    Kobayashi, T.
    Oya, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/206228.pdf
    Data publikacji:
    2003
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie sprzężone Burgersów
    stabilizacja globalna
    regulacja adaptacyjna
    sterowanie nieliniowe brzegowe
    coupled Burgers' equation
    global stabilization
    adaptive regulation
    nonlinear boundary control
    Opis:
    This paper is concerned with adaptive stabilization of two coupled viscous Burgers' equations by nonlinear boundary controllers. Under the existence of bounded deterministic disturbances, the adaptive controllers are constructed by the concept of high-gain nonlinear output feedback and the estimation mechanism of the unknown parameters. In the controlled system the global stability and the convergence of the system states to zero will be guaranteed. It is shown that the theory can be generalized to the systems with higher-order nonlinearity.
    Źródło:
    Control and Cybernetics; 2003, 32, 2; 245-258
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Impact of Boundary Conditions on Acoustic Excitation of Entropy Perturbations in a Bounded Volume of Newtonian Gas
    Autorzy:
    Perelomova, Anna
    Powiązania:
    https://bibliotekanauki.pl/articles/177071.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    nonlinear acoustics
    acoustic heating in resonators
    Burgers equation
    first type
    second type
    boundary conditions
    acoustic heating in a half-space
    Opis:
    Excitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoretically considered in this work. The dynamic equation for an excess density which specifies the entropy mode, has been obtained by means of the method of projections. It takes the form of the diffusion equation with an acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient is proportional to the thermal conduction, and the acoustic force is proportional to the total attenuation. Theoretical description of instantaneous heating allows to take into account aperiodic and impulsie sounds. Acoustic heating in a half-space and in a planar resonator is discussed. The aim of this study is to evaluate acoustic heating and determine the contribution of thermal conduction and mechanical viscosity in different boundary problems. The conclusions are drawn for the Dirichlet and Neumann boundary conditions. The instantaneous dynamic equation for variations in temperature, which specifies the entropy mode, is solved analytically for some types of acoustic exciters. The results show variation in temperature as a function of time and distance from the boundary for different boundary conditions.
    Źródło:
    Archives of Acoustics; 2019, 44, 2; 321-328
    0137-5075
    Pojawia się w:
    Archives of Acoustics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions
    Autorzy:
    Kindybaliuk, A.
    Prytula, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/122896.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    nonlinear dynamical system
    conservation laws
    implectic operators
    method of undetermined coefficients
    differential algebraic algorithm
    combined algorithm
    finite dimensional reduction
    Hamiltonian system
    exact solutions
    Boussinesq-Burgers equation
    nieliniowy układ dynamiczny
    prawa zachowania
    algebraiczny algorytm różniczkowy
    system Hamiltona
    rozwiązania dokładne
    równanie Boussinesqa-Burgersa
    Opis:
    In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 3; 85-99
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Group invariant solution of some time fractional evolution equations
    Autorzy:
    Mandal, H.
    Bira, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/122890.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional coupled Burger’s equation
    fractional DSSH equations
    Riemann Liouville’s fractional derivative
    Erdélyi-Kober operator
    symmetry analysis
    exact solution
    równania ewolucji
    ułamkowe równania różniczkowe
    ułamkowe równania DSSH
    pochodna ułamkowa Riemanna Liouville'a
    operator Erdélyi-Kober
    Opis:
    In this paper, we consider some classes of a system of nonlinear fractional differential equations (FDEs) arising in some important physical phenomena. Using symmetry group of transformations, the given systems of fractional partial differential equations (FPDEs) are reduced to systems of fractional ordinary differential equations (FODEs). Further, using the group invariant condition, we solve the reduced systems of FODEs and exact solutions of the given equations are constructed. Finally, the physical significance of the solutions are investigated graphically based on the exact solutions in order to highlight the importance of the study.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 35-46
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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