PROBLEMA CAUCHY PENTRU UN SISTEM PARABOLIC DE ECUAȚII INTEGRO DIFERENȚIALE CU UN OPERATOR  DE TIP VOLTERRA-FREDHOLM

I. M. DANYLIUK; A. O. DANYLIUK

doi:10.36120/2587-3644.v8i2.29-42

Vol 8 No 2 (2019), Статьи

Vol 8 No 2 (2019)

THE CAUCHY PROBLEM FOR A PARABOLIC SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS WITH AN OPERATOR OF VOLTERRA-FREDHOLM TYPE

Статьи

https://doi.org/10.36120/2587-3644.v8i2.29-42

Published January 28, 2020

I. M. DANYLIUK⁺⁻
A. O. DANYLIUK⁺⁻

I. M. DANYLIUK

Yuriy Fedkovych Chernivtsi National University

A. O. DANYLIUK

Chernivtsi gymnasium 2

Supplementary Files

pdf (Русский)

Keywords

parabolic system of integro-dierential equations, Volterra-Fredholm operator, fun- damental matrix of solutions, method of reduction to a system of integral equations, kernels of the integral operator, resolvent, conditions for correct solvability.

How to Cite

DANYLIUK, I. M., & DANYLIUK, A. O. (2020). THE CAUCHY PROBLEM FOR A PARABOLIC SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS WITH AN OPERATOR OF VOLTERRA-FREDHOLM TYPE. Acta Et Commentationes Exact and Natural Sciences, 8(2), 29-42. https://doi.org/10.36120/2587-3644.v8i2.29-42

Abstract

The Cauchy problem for a parabolic system of integro-dierential equations with an operator of Volterra-Fredholm type is considered. A fundamental matrix of solutions of the problem in classical Holder spaces is constructed, the estimates for the matrix and its derivatives are established. This makes it possible to prove the correctness theorem.