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Iterative methods for parabolic functional differential equations

100%

Matusik M.

Applicationes Mathematicae

2013

tom 40

nr 2

221-235

This paper is concerned with iterative methods for parabolic functional differential equations with initial boundary conditions. Monotone iterative methods are discussed. We prove a theorem on the existence of solutions for a parabolic problem whose right-hand side admits a Jordan type decomposition with respect to the function variable. It is shown that there exist Newton sequences which converge to the solution of the initial problem. Differential equations with deviated variables and differential integral equations can be obtained from our general model by specializing given operators.

Existence of classical solutions for parabolic functional differential equations with initial boundary conditions of Robin type

100%

Matusik M.

Annales Polonici Mathematici

2012

tom 105

nr 3

253-265

The paper deals with the initial boundary value problem of Robin type for parabolic functional differential equations. The unknown function is the functional variable in the equation and the partial derivatives appear in the classical sense. A theorem on the existence of a classical solution is proved. Our formulation and results cover differential equations with deviated variables and differential integral problems.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Applicationes Mathematicae

2 Matusik M.

1 2013

1 2012

Wyniki wyszukiwania

Iterative methods for parabolic functional differential equations

Existence of classical solutions for parabolic functional differential equations with initial boundary conditions of Robin type