The first boundary value problem for
coupled diffusion systems 
with functional arguments

P.P. Babak

This paper discusses the existence and uniqueness theorem for the problem containing the initial boundary value problem for a parabolic system coupled with the initial problem for a system of ordinary differential equations. The system of equations contains a functional on continuous functions of space arguments.

1. Крянев А.В., Шихов С.Б. Вопросы математической теории реакторов. Нелинейный анализ. — М., 1983.

2. Pell T.M., Davis T.G. Diffusion and reaction in polyester melts // J. Polym. Science. 1973. Vol.11. P.1671–1682.

3. Fitzhugh R. Impulses and physiological states in models of nerve membrane // Biophys. J. 1961. Vol.1. P.445–466.

4. Hodgkin A.L., Huxley A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve // J. Physiol. 1952. Vol.117. P.500–544.

5. McNabb A. Comparison and existence theorems for multicomponent diffusion systems // J. Math. Anal. Appl. 1961. Vol.3, No.1. P.133–144.

6. Масленникова В.Н. Первая краевая задача для некоторых квазилинейных систем математической теории диффузии // Журнал вычисл. матем. и матем. физики. 1963. Т.3, №3. С.467–477.

7. Ugovski H. On integro-differential equations of parabolic and elliptic type // Ann. Polon. Math. 1970. Vol.22, No.3. P.255–275.

8. Ugovski H. Some theorems on the estimate and existence of solutions of integro-differential equations of parabolic type // Ann. Polon. Math. 1972. Vol.25, No.3. P.311–323.

9. Фридман А. Уравнения с частными производными параболического типа. — М.: Мир, 1968. 428 с.

10. Friedman A. On quasi-linear parabolic equations of the second order. II // J. Math. and Mech. 1960. Vol.9, No.4. P.539–556.

	The first boundary value problem for coupled diffusion systems with functional arguments
Author	P.P. Babak 290602, Lviv, Universytetska str., 1,Lviv University, Department of Mathematics and Mechanics
Abstract	This paper discusses the existence and uniqueness theorem for the problem containing the initial boundary value problem for a parabolic system coupled with the initial problem for a system of ordinary differential equations. The system of equations contains a functional on continuous functions of space arguments.
Keywords	existence and uniqueness theorem, initial boundary value problem, parabolic system, ordinary differential equations
DOI	doi:10.30970/ms.7.2.179-186
Reference	1. Крянев А.В., Шихов С.Б. Вопросы математической теории реакторов. Нелинейный анализ. — М., 1983. 2. Pell T.M., Davis T.G. Diffusion and reaction in polyester melts // J. Polym. Science. 1973. Vol.11. P.1671–1682. 3. Fitzhugh R. Impulses and physiological states in models of nerve membrane // Biophys. J. 1961. Vol.1. P.445–466. 4. Hodgkin A.L., Huxley A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve // J. Physiol. 1952. Vol.117. P.500–544. 5. McNabb A. Comparison and existence theorems for multicomponent diffusion systems // J. Math. Anal. Appl. 1961. Vol.3, No.1. P.133–144. 6. Масленникова В.Н. Первая краевая задача для некоторых квазилинейных систем математической теории диффузии // Журнал вычисл. матем. и матем. физики. 1963. Т.3, №3. С.467–477. 7. Ugovski H. On integro-differential equations of parabolic and elliptic type // Ann. Polon. Math. 1970. Vol.22, No.3. P.255–275. 8. Ugovski H. Some theorems on the estimate and existence of solutions of integro-differential equations of parabolic type // Ann. Polon. Math. 1972. Vol.25, No.3. P.311–323. 9. Фридман А. Уравнения с частными производными параболического типа. — М.: Мир, 1968. 428 с. 10. Friedman A. On quasi-linear parabolic equations of the second order. II // J. Math. and Mech. 1960. Vol.9, No.4. P.539–556.
Pages	179-186
Volume	7
Issue	2
Year	1997
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

The first boundary value problem for coupled diffusion systems with functional arguments