Using operators of fractional integration and differentiation, we prove a theorem on the wellposedness of a general parabolic boundary-value problem for a system of integro-differential equations with integral operators in boundary conditions.
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S. D. Éidel’man, Parabolic Systems [in Russian], Nauka, Moscow (1964).
T. Ya. Zagorskii, Mixed Problem for a System of Partial Differential Equations of Parabolic Type [in Russian], Lviv University, Lviv (1961).
V. A. Solonnikov, “On boundary-value problems for linear parabolic systems of differential equations of general form,” Tr. Mat. Inst. Akad. Nauk SSSR, 83, 3–162 (1965).
S. D. Ivasishen, Green Matrices of Parabolic Problems [in Russian], Vyshcha Shkola, Kiev (1990).
M. I. Matviichuk, Singular Parabolic Boundary-Value Problems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (1999).
A. O. Danylyuk, “On the fundamental matrix of solutions of the Cauchy problem for a parabolic system of integro-differential equations,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 349, 18–24 (2007).
A. Friedman, Partial Differential Equations of Parabolic Type [Russian translation], Mir, Moscow (1968).
M. I. Matviichuk, Parabolic and Elliptic Boundary-Value Problems with Singularities [in Ukrainian], Prut, Chernivtsi (2003).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1610 – 1618, December, 2008.
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Danylyuk, A.O. Boundary-value problem for a parabolic system of integro-differential equations with integral conditions. Ukr Math J 60, 1889–1900 (2008). https://doi.org/10.1007/s11253-009-0178-0
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DOI: https://doi.org/10.1007/s11253-009-0178-0