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Wyświetlanie 1-15 z 26
Tytuł:
On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables
Autorzy:
Człapiński, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/1294572.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
differential-functional equations
nonlinear hyperbolic problems
nonlocal conditions
Opis:
We seek for classical solutions to hyperbolic nonlinear partial differential-functional equations of the second order. We give two theorems on existence and uniqueness for problems with nonlocal conditions in bounded and unbounded domains.
Źródło:
Annales Polonici Mathematici; 1997, 67, 3; 205-214
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and continuous dependence for a class of neutral functional differential equations
Autorzy:
Faina, Loris
Powiązania:
https://bibliotekanauki.pl/articles/1310936.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
neutral functional differential equations
abstract equivalence
Opis:
A general result on existence and continuous dependence of the solution for a quite wide class of N.F.D.E. is given. Further, an abstract equivalence is proved for three different formulations of N.F.D.E.
Źródło:
Annales Polonici Mathematici; 1996, 64, 3; 215-226
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Neumann’s condition
Autorzy:
Sapa, Lucjan
Powiązania:
https://bibliotekanauki.pl/articles/962640.pdf
Data publikacji:
2009
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
parabolic differential functional equations
difference methods
nonlinear estimates of the generalized Perron type
Opis:
Classical solutions of nonlinear second-order partial differential functional equations of parabolic type with Neumann’s condition are approximated in the paper by solutions of associated explicit difference functional equations. The functional dependence is of the Volterra type. Nonlinear estimates of the generalized Perron type for given functions are assumed. The convergence and stability results are proved with the use of the comparison technique. These theorems in particular cover quasi-linear equations, but such equations are also treated separately. The known results on similar difference methods can be obtained as particular cases of our simple result.
Źródło:
Commentationes Mathematicae; 2009, 49, 1; 83-106
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type
Autorzy:
Zabawa, T.S.
Powiązania:
https://bibliotekanauki.pl/articles/255205.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite systems
elliptic differential-functional equations
monotone iterative technique
Chaplygin's method
Dirichlet problem
Opis:
The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and uper functions.
Źródło:
Opuscula Mathematica; 2005, 25, 2; 333-343
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
Autorzy:
Zabawa, T.S.
Powiązania:
https://bibliotekanauki.pl/articles/254967.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
stability of solutions
infinite systems
parabolic equations
elliptic equations
semilinear differential-functional equations
monotone iteration method
Opis:
A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as t → ∞ is the solution of the associated elliptic problem. The result is based on the monotone methods.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 173-183
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical methods for hyperbolic differential functional problems
Autorzy:
Ciarski, R.
Powiązania:
https://bibliotekanauki.pl/articles/255099.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
functional differential equations
stability and convergence
Opis:
The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.
Źródło:
Opuscula Mathematica; 2008, 28, 1; 29-46
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Newton’s method for first-order stochastic functional partial differential equations
Autorzy:
Wrzosek, Monika
Powiązania:
https://bibliotekanauki.pl/articles/963678.pdf
Data publikacji:
2014
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
stochastic functional partial differential equations
Opis:
We apply Newton’s method to hyperbolic stochastic functional partial differential equations of the first order driven by a multidimensional Brownian motion. We prove a first-order convergence and a second-order convergence in a probabilistic sense.
Źródło:
Commentationes Mathematicae; 2014, 54, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
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:
Difference methods for infinite systems of hyperbolic functional differential equations on the Haar pyramid
Autorzy:
Jaruszewska-Walczak, D.
Powiązania:
https://bibliotekanauki.pl/articles/2050179.pdf
Data publikacji:
2004
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
initial problems
infinite systems of differential functional equations
difference functional inequalities
nonlinear estimates of Perron type
Opis:
We consider the Cauchy problem for infinite system of differential functional equations $\partial_{t}z_{k}(t, x) = f_{k}(t, x, z, \partial_{x}z_{k}(t, x)), k \in \mathbf{N}$. In the paper we consider a general class of difference methods for this problem. We prove the convergence of methods under the assumptions that given functions satisfy the nonlinear estimates of the Perron type with respect to functional variables. The proof is based on functional difference inequalities. We constructed the Euler method as an example of difference method.
Źródło:
Opuscula Mathematica; 2004, 24, 1; 85-96
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations
Autorzy:
Brzychczy, Stanisław
Powiązania:
https://bibliotekanauki.pl/articles/1293995.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
method of lower and upper functions
infinite systems of parabolic differential-functional equations
monotone iterative method
Opis:
We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.
Źródło:
Annales Polonici Mathematici; 1999, 72, 1; 15-24
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the local Cauchy problem for nonlinear hyperbolic functional differential equations
Autorzy:
Człapiński, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/1294574.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
functional differential equations
weak solutions
bicharacteristics
successive approximations
Opis:
We consider the local initial value problem for the hyperbolic partial functional differential equation of the first order (1) $Dₓz(x,y) = f(x,y,z(x,y),(Wz)(x,y),D_y z(x,y))$ on E, (2) z(x,y) = ϕ(x,y) on [-τ₀,0]×[-b,b], where E is the Haar pyramid and τ₀ ∈ ℝ₊, b = (b₁,...,bₙ) ∈ ℝⁿ₊. Using the method of bicharacteristics and the method of successive approximations for a certain functional integral system we prove, under suitable assumptions, a theorem on the local existence of weak solutions of the problem (1),(2).
Źródło:
Annales Polonici Mathematici; 1997, 67, 3; 215-232
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Classical solutions of initial problems for quasilinear partial functional differential equations of the first order
Autorzy:
Czernous, W.
Powiązania:
https://bibliotekanauki.pl/articles/254909.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
partial functional differential equations
classical solutions
local existence
bicharacteristics
Opis:
We consider the initial problem for a quasilinear partial functional differential equation of the first order [formula], z(t, x) = varphi(t, x) ((t, x) ∈ [-h0, 0] x Rn) where z(t, x) : [-h0, 0] x [-h, h] → R is a function defined by z(t, x) (τ, ξ) = z(t + τ, + ξ) for (τ, ξ) ∈ [-h0, 0] x [-h, h]. Using the method of bicharacteristics and the fixed-point theorem we prove, under suitable assumptions, a theorem on the local existence and uniqueness of classical solutions of the problem and its continuous dependence on the initial condition.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 13-29
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Differential difference inequalities related to parabolic functional differential equations
Autorzy:
Netka, M.
Powiązania:
https://bibliotekanauki.pl/articles/255915.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
parabolic functional differential equations
method of lines
stability and convergence
Opis:
Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the method of lines is given. Nonlinear estimates of the Perron type for given operators with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables.
Źródło:
Opuscula Mathematica; 2010, 30, 1; 95-115
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
Autorzy:
Brzychczy, S.
Powiązania:
https://bibliotekanauki.pl/articles/255097.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite systems
reaction-diffusion-convection equations
semilinear parabolic differential-functional equations
Volterra functionals
monotone iterative methods
method of upper and lower solutions
Opis:
We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form [formula] where [formula] in a bounded cylindrical domain (0, T] x G := D rcup Rm+1. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
Źródło:
Opuscula Mathematica; 2005, 25, 1; 29-99
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Uniqueness of solutions of a generalized Cauchy problem for a system of first order partial functional differential equations
Autorzy:
Netka, M.
Powiązania:
https://bibliotekanauki.pl/articles/952848.pdf
Data publikacji:
2009
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
functional differential equations
comparison methods
nonlinear estimates of Perron type
Opis:
The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A method of integral functional inequalities is used.
Źródło:
Opuscula Mathematica; 2009, 29, 1; 69-79
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 26

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