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1
Content available Existence and regularity of solutions for hyperbolic functional differential problems
Kamont Z.
Opuscula Mathematica
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2014
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Vol. 34, no. 2
217--242
EN
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.
2
Content available Numerical approximations of difference functional equations and applications
Kamont Z.
Opuscula Mathematica
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2005
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Vol. 25, no. 1
109-130
EN
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.
3
Content available remote Generalized Euler method for nonlinear first order partial differential functional equations
Kamont Z., Nadolski A.
Demonstratio Mathematica
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2005
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Vol. 38, nr 4
976-996
EN
Classical solutions of the local Cauchy problem on the Haar pyramid are approximated in the paper by solutions of suitable quasilinear systems of difference equations. The proof of the stability of the difference problem is based on a comparison technique with nonlinear estimates of the Perron type. This new approach to the numerical solving of nonlinear functional differential equations is generated by a quasilinearization method for initial problems. Numerical examples are given.
4
Content available remote Numerical approximation of first order partial differential equations with deviated variables
Baranowska A., Kamont Z.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2003
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[Z] 43(1)
1-31
EN
Classical solutions of the local Cauchy problem on the Haar pyramid are approximated in the paper by solutions of suitable quasilinear systems of difference equations. The proof of the stability of the difference problem is based on a comparison technique with nonlinear estimates of the Perron type. This new approach to the numerical solving of nonlinear equations with deviated variables is generated by a quasilinearization method for initial problems. Numerical examples are given.
5
Content available remote Równania różniczkowe paraboliczne w pracach Profesora Piotra Besali
Kamont Z.
Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
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1999
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[Z] 35
55-80
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