Kushnirenko S. V.
On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations
Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1699 – 1706
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.