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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 12, pp. 1699 – 1706, December, 2004.
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Kulinich, H.L., Kushnirenko, S.V. On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations. Ukr Math J 56, 2007–2016 (2004). https://doi.org/10.1007/s11253-005-0165-z
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DOI: https://doi.org/10.1007/s11253-005-0165-z