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

Authors

  • G. L. Kulinich
  • S. V. Kushnirenko

Abstract

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.

Published

25.12.2004

Issue

Section

Short communications

How to Cite

Kulinich, G. L., and S. V. Kushnirenko. “On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations”. Ukrains’kyi Matematychnyi Zhurnal, vol. 56, no. 12, Dec. 2004, pp. 1699 – 1706, https://umj.imath.kiev.ua/index.php/umj/article/view/3877.