Browsing by Subject "functional differential equations"

Now showing 1 - 5 of 5

Access status: Open Access ,
Existence and regularity of solutions for hyperbolic functional differential problems
(2014) Kamont, Zdzisław
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.
Access status: Open Access ,
Numerical approximations of difference functional equations and applications
(2005) Kamont, Zdzisław
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.
Access status: Open Access ,
Numerical methods for hyperbolic differential functional problems
(2008) Ciarski, Roman
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.
Access status: Open Access ,
On the quasilinear Cauchy problem for a hyperbolic functional differential equation
(2015) Puźniakowska-Gałuch, Elżbieta
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.
Access status: Open Access ,
Uniqueness of solutions of a generalized Cauchy problem for a system of first order partial functional differential equations
(2009) Netka, Milena
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.