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On the solvability of a system of two multidimensional loaded parabolic equations with the Cauchy data

Galina V. Romanenko, Igor V. Frolenkov

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: We study a multidimensional system of two loaded parabolic equations of a special kind with the Cauchy data. Sufficient conditions for the existence of a solution in the class of smooth bounded functions are obtained. The splitting method at differential level (the method of weak approximation) is used in the proof.

Keywords: inverse problem, direct problem, loaded equation, parabolic equation, weak approximation method, system of partial differential equations, Cauchy problem.

UDC: 517.9

Received: 17.01.2016
Received in revised form: 03.04.2016
Accepted: 15.06.2016

Language: English

DOI: 10.17516/1997-1397-2016-9-3-364-373

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