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Wyświetlanie 1-15 z 26
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:
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:
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:
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:
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:
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
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:
On extremal solutions of differential equations with advanced argument
Autorzy:
Augustynowicz, Antoni
Jankowski, Jan
Powiązania:
https://bibliotekanauki.pl/articles/746206.pdf
Data publikacji:
2006
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
functional differential equations
advanced argument
extremal solutions
Darboux problem
Carathéodory condition
Opis:
We obtain existence of absolutely continuous extremal solutions of the problem \(u'(x) = F(x, u(x), u(h(x)))\), \(u(0) = u_0\), and the Darboux problem for \(u_{xy}(x, y) = G(x, y, u(x, y), u(H(x, y)))\), where \(h\) and \(H\) are arbitrary continuous deviated arguments.
Źródło:
Commentationes Mathematicae; 2006, 46, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical approximations of parabolic functional differential equations on unbounded domains
Autorzy:
Baranowska, Anna
Powiązania:
https://bibliotekanauki.pl/articles/745298.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
functional differential equations
stability and convergence
nonlinear estimates of the Perron type
Opis:
The paper is concerned with initial problems for nonlinear parabolic functional differential equations. A general class of difference methods is constructed. A theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type with an unknown function of several variables is presented. The convergence of explicit difference schemes is proved by means of consistency and stability arguments. It is assumed that given function satisfy nonlinear estimates of the Perron type with respect to a functional variable. Results obtained in the paper can be applied to differential integral problems and equations with retarded variables. Numerical examples are presented.
Źródło:
Commentationes Mathematicae; 2007, 47, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the quasilinear Cauchy problem for a hyperbolic functional differential equation
Autorzy:
Puźniakowska-Gałuch, E.
Powiązania:
https://bibliotekanauki.pl/articles/254975.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
functional differential equations
Haar pyramid
differentiability of solutions
Fredholm type of equation
Opis:
The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions defined on the Haar pyramid is proved. A result on differentiability of a solution with respect to initial data is proved.
Źródło:
Opuscula Mathematica; 2015, 35, 6; 915-933
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical approximations of difference functional equations and applications
Autorzy:
Kamont, Z.
Powiązania:
https://bibliotekanauki.pl/articles/255105.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
functional differential equations
stability and convergence
interpolating operators
nonlinear estimates of Perron type
Opis:
We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
Źródło:
Opuscula Mathematica; 2005, 25, 1; 109-130
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and regularity of solutions for hyperbolic functional differential problems
Autorzy:
Kamont, Z.
Powiązania:
https://bibliotekanauki.pl/articles/255366.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
functional differential equations
weak solutions
Haar pyramid
differentiability with respect to initial functions
Opis:
A generalized Cauchy problem for quasilinear hyperbolic functional differential systems is considered. A theorem on the local existence of weak solutions is proved. The initial problem is transformed into a system of functional integral equations for an unknown function and for their partial derivatives with respect to spatial variables. The existence of solutions for this system is proved by using a method of successive approximations. We show a theorem on the differentiability of solutions with respect to initial functions which is the main result of the paper.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 217-242
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Classical solutions of mixed problems for quasilinear first order PFDEs on a cylindrical domain
Autorzy:
Czernous, W.
Powiązania:
https://bibliotekanauki.pl/articles/255887.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
partial functional differential equations
classical solutions
local existence
characteristcs
cylindrical domain
a priori estimates
Opis:
We abandon the setting of the domain as a Cartesian product of real intervals, customary for first order PFDEs (partial functional differential equations) with initial boundary conditions. We give a new set of conditions on the possibly unbounded domain Ω with Lipschitz differentiable boundary. Well-posedness is then reliant on a variant of the normal vector condition. There is a neighbourhood of ∂Ω with the property that if a characteristic trajectory has a point therein, then its every earlier point lies there as well. With local assumptions on coefficients and on the free term, we prove existence and Lipschitz dependence on data of classical solutions on (0,c)×Ω to the initial boundary value problem, for small c. Regularity of solutions matches this domain, and the proof uses the Banach fixed-point theorem. Our general model of functional dependence covers problems with deviating arguments and integro-differential equations.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 291-310
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Difference problems generated by infinite systems of nonlinear parabolic functional differential equations with the Robin conditions
Autorzy:
Czernous, W.
Jaruszewska-Walczak, D.
Powiązania:
https://bibliotekanauki.pl/articles/255694.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
nonlinear parabolic equations
functional differential equations
infinite systems
Volterra type operators
nonlinear estimates of Perron type
truncation methods
Opis:
We consider the classical solutions of mixed problems for infinite, countable systems of parabolic functional differential equations. Difference methods of two types are constructed and convergence theorems are proved. In the first type, we approximate the exact solutions by solutions of infinite difference systems. Methods of second type are truncation of the infinite difference system, so that the resulting difference problem is finite and practically solvable. The proof of stability is based on a comparison technique with nonlinear estimates of the Perron type for the given functions. The comparison system is infinite. Parabolic problems with deviated variables and integro-differential problems can be obtained from the general model by specifying the given operators.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 311-326
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Wyświetlanie 1-15 z 26

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