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.
The research for this paper was carried out in Siberian Federal University within the framework of the project "Multidimensional Complex Analysis and Differential Equations" funded by the grant of the Russian Federation Government to support scientific research under supervision of a leading scientist, no. 14.Y26.31.0006.
Received: 17.01.2016 Received in revised form: 03.04.2016 Accepted: 15.06.2016
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: English
Citation:
Galina V. Romanenko, Igor V. Frolenkov, “On the solvability of a system of two multidimensional loaded parabolic equations with the Cauchy data”, J. Sib. Fed. Univ. Math. Phys., 9:3 (2016), 364–373
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\pages 364--373
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Linking options:
https://www.mathnet.ru/eng/jsfu495
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This publication is cited in the following 1 articles:
I. V. Frolenkov, E. N. Kriger, “On the solvability of the Cauchy problem for a certain class of multidimensional loaded parabolic equations”, J. Math. Sci. (N. Y.), 254:6 (2021), 743–760
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