# On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations

### Abstract

We consider a solution of the Cauchy problem*u*(

*t, x*),

*t*> 0,

*x*∈

*R*

^{2}, for one class of integro-differential equations. These equations have the following specific feature: the matrix of the coefficients of higher derivatives is degenerate for all

*x*. We establish conditions for the existence of the limit lim

_{ t→∞}

*u*(

*t, x*) =

*v*(

*x*) and represent the solution of the Cauchy problem in explicit form in terms of the coefficients of the equation.

Published

25.12.2004

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 56, no. 12, Dec. 2004, pp. 1699 -, https://umj.imath.kiev.ua/index.php/umj/article/view/3877.

Issue

Section

Short communications