2019
Том 71
№ 8

All Issues

Kushnirenko S. V.

Articles: 1
Brief Communications (Ukrainian)

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

Kulinich G. L., Kushnirenko S. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1699 – 1706

We consider a solution of the Cauchy problem u(t, x), t > 0, xR 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.