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Wyszukujesz frazę "nonlinear elliptic equations" wg kryterium: Temat

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    Wyświetlanie 1-10 z 10
    Tytuł:
    An existence and approximation theorem for solutions of degenerate nonlinear elliptic equations
    Autorzy:
    Cavalheiro, Albo Carlos
    Powiązania:
    https://bibliotekanauki.pl/articles/747200.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Degenerate nonlinear elliptic equations
    weighted Sobolev spaces
    Opis:
    The main result establishes that a weak solution of degenerate nonlinear  elliptic equations can be approximated by a sequence of solutions for non-degenerate nonlinear elliptic equations.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2018, 72, 1
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations
    Autorzy:
    Cavalheiro, Albo Carlos
    Powiązania:
    https://bibliotekanauki.pl/articles/747202.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Degenerate nonlinear elliptic equations
    weighted Sobolev spaces
    Opis:
    In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations \begin{align} {\Delta}(v(x)\, {\vert{\Delta}u\vert}^{p-2}{\Delta}u) &-\sum_{j=1}^n D_j{\bigl[}{\omega}_1(x) \mathcal{A}_j(x, u, {\nabla}u){\bigr]}+ b(x,u,{\nabla}u)\, {\omega}_2(x)\\ & = f_0(x) - \sum_{j=1}^nD_jf_j(x), \ \ {\rm in } \ \ {\Omega} \end{align} in the setting of the weighted Sobolev spaces.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2016, 70, 2
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and uniqueness of the solutions of some degenerate nonlinear elliptic equations
    Autorzy:
    Cavalheiro, A. C
    Powiązania:
    https://bibliotekanauki.pl/articles/255079.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    degenerate nonlinear elliptic equations
    weighted Sobolev spaces
    Opis:
    In this paper we are interested in the existence of solutions for the Dirichlet problem associated with degenerate nonlinear elliptic equations [formula] in the setting of the weighted Sobolev spaces [formula].
    Źródło:
    Opuscula Mathematica; 2014, 34, 1; 15-28
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlocal elliptic problems
    Autorzy:
    Krzywicki, Andrzej
    Nadzieja, Tadeusz
    Powiązania:
    https://bibliotekanauki.pl/articles/1207643.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonlinear nonlocal elliptic equations
    Opis:
    Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem $-Δφ = M f(φ)/((∫_{Ω} f(φ))^p)$, $φ|_{\partial Ω}=0$ are given.
    Źródło:
    Banach Center Publications; 2000, 52, 1; 147-152
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On optimal and quasi-optimal controls in coefficients for multi-dimensional thermistor problem with mixed Dirichlet-Neumann boundary conditions
    Autorzy:
    Kogut, Peter I.
    Powiązania:
    https://bibliotekanauki.pl/articles/970117.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nonlinear elliptic equations
    control in coefficients
    p(x)-Laplacian
    approximation approach
    thermistor problem
    Opis:
    In this paper we deal with an optimal control problem in coefficients for the system of two coupled elliptic equations, also known as the thermistor problem, which provides a simultaneous description of the electric field u = u(x) and temperature θ(x). The coefficients of the operator div (B(x)∇θ(x)) are used as the controls in L∞(Ω). The optimal control problem is to minimize the discrepancy between a given distribution θd ∈ Lr(Ω) and the temperature of thermistor θ ∈ W1,γ 0 (Ω) by choosing an appropriate anisotropic heat conductivity matrix B. Basing on the perturbation theory of extremal problems and the concept of fictitious controls, we propose an “approximation approach” and discuss the existence of the so-called quasi-optimal and optimal solutions to the given problem.
    Źródło:
    Control and Cybernetics; 2019, 48, 1; 31-68
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Mesh-Independence Principle for Quadratic Penalties Applied to Semilinear Elliptic Boundary Control
    Autorzy:
    Grossman, Christian
    Winkler, Max
    Powiązania:
    https://bibliotekanauki.pl/articles/1373554.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
    Tematy:
    optimal boundary control
    mesh-independence principle
    penalty methods for control constraints
    weakly nonlinear elliptic equations
    Opis:
    The quadratic loss penalty is a well known technique for optimization and control problems to treat constraints. In the present paper they are applied to handle control bounds in a boundary control problems with semilinear elliptic state equations. Unlike in the case of finite dimensional optimization for infinite dimensional problems the order of convergence could only be roughly estimated, but numerical experiments revealed a clearly better convergence behavior with constants independent of the dimension of the used discretization. The main result in the present paper is the proof of sharp convergence bounds for both, the finite und infinite dimensional problem with a mesh-independence in case of the discretization. Further, to achieve an efficient realization of penalty methods the principle of control reduction is applied, i.e. the control variable is represented by the adjoint state variable by means of some nonlinear function. The resulting optimality system this way depends only on the state and adjoint state. This system is discretized by conforming linear finite elements. Numerical experiments show exactly the theoretically predicted behavior of the studied penalty technique.
    Źródło:
    Schedae Informaticae; 2012, 21; 9-26
    0860-0295
    2083-8476
    Pojawia się w:
    Schedae Informaticae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of solution of the nonlinear Dirichlet problem for differential-functional equations of elliptic type
    Autorzy:
    Brzychczy, Stanisław
    Powiązania:
    https://bibliotekanauki.pl/articles/1311834.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonlinear differential-functional equations of elliptic type
    monotone iterative technique
    Chaplygin's method
    Dirichlet problem
    Opis:
    Consider a nonlinear differential-functional equation (1) Au + f(x,u(x),u) = 0 where $Au := ∑_{i,j=1}^m a_{ij}(x) (∂²u)/(∂x_i ∂x_j)$, $x=(x_1,...,x_m) ∈ G ⊂ ℝ^m$, G is a bounded domain with $C^{2+α}$ (0 < α < 1) boundary, the operator A is strongly uniformly elliptic in G and u is a real $L^p(G̅)$ function. For the equation (1) we consider the Dirichlet problem with the boundary condition (2) u(x) = h(x) for x∈ ∂G. We use Chaplygin's method [5] to prove that problem (1), (2) has at least one regular solution in a suitable class of functions. Using the method of upper and lower functions, coupled with the monotone iterative technique, H. Amman [3], D. H. Sattinger [13] (see also O. Diekmann and N. M. Temme [6], G. S. Ladde, V. Lakshmikantham, A. S. Vatsala [8], J. Smoller [15]) and I. P. Mysovskikh [11] obtained similar results for nonlinear differential equations of elliptic type. A special case of (1) is the integro-differential equation $Au + f(x,u(x), ∫_G u(x)dx) = 0$. Interesting results about existence and uniqueness of solutions for this equation were obtained by H. Ugowski [17].
    Źródło:
    Annales Polonici Mathematici; 1993, 58, 2; 139-146
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Travelling wave solutions of the non-linear wave equations
    Autorzy:
    Haider, Jamil A.
    Rahman, Jamshaid U.
    Zaman, Fiazud D.
    Gul, Sana
    Powiązania:
    https://bibliotekanauki.pl/articles/2204690.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    nonlinear evolution problems
    coupled equations
    Jacobi elliptic functions
    periodic solutions
    Opis:
    This article focuses on the exact periodic solutions of nonlinear wave equations using the well-known Jacobi elliptic function expansion method. This method is more general than the hyperbolic tangent function expansion method. The periodic solutions are found using this method which contains both solitary wave and shock wave solutions. In this paper, the new results are computed using the closed-form solution including solitary or shock wave solutions which are obtained using Jacobi elliptic function method. The corresponding solitary or shock wave solutions are compared with the actual results. The results are visualised and the periodic behaviour of the solution is described in detail. The shock waves are found to break with time, whereas, solitary waves are found to be improved continuously with time.
    Źródło:
    Acta Mechanica et Automatica; 2023, 17, 2; 239--245
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical simulation of liquid motion in a partly filled tank
    Autorzy:
    Warmowska, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255682.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonlinear boundary value problem
    linear elliptic equations
    sloshing
    free-surface potential flows
    Opis:
    The paper presents the problem of liquid motion in a 2D partly filled tank. It is assumed that the flow of liquid in tank is a potential, hence it can be described by Laplace equations with appropriate boundary conditions. The problem is solved using the boundary element method. The developed numerical algorithm makes it possible to determine the free surface elevation, the velocity field and the pressure field during the liquid motion in the tank. The area occupied by liquid is represented by a mesh changing in time. Numerical computations are performed for translatory and rotational motion of the tank. The results of numerical computations are verified by experiment.
    Źródło:
    Opuscula Mathematica; 2006, 26, 3; 529-540
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a semilinear elliptic eigenvalue problem
    Autorzy:
    Coclite, Mario
    Powiązania:
    https://bibliotekanauki.pl/articles/1294623.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    semilinear elliptic equations
    nonlinear boundary-value problems
    positive solutions
    supersolution and subsolution method
    Opis:
    We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, $u|_{∂Ω} = 0$, where f(x) and h(u) satisfy minimal regularity assumptions.
    Źródło:
    Annales Polonici Mathematici; 1997, 67, 3; 289-295
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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