Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 156, Pages 41–57 (Mi into396)  
On the solvability of the Cauchy problem for a certain class of multidimensional loaded parabolic equations

I. V. Frolenkova, E. N. Krigerb

a Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk
b JSC Information Satellite Systems Reshetnev, Zheleznogorsk, Krasnoyarsk Krai, Russia
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Abstract: In this paper, we examine the solvability of a new class of nonclassical direct problems for multidimensional loaded parabolic equations with Cauchy data. We obtain sufficient conditions for the solvability of the problem; the proof is based on the method of weak approximation. By an example, we demonstrate the application of the theorem proved to the study of inverse problems for multidimensional parabolic equations with Cauchy data.
Keywords: parabolic equation, loaded equation, Cauchy problem, solvability, method of weak approximation.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 254, Issue 6, Pages 743–760
DOI: https://doi.org/10.1007/s10958-021-05337-y
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35K15, 35B45, 35B65
Language: Russian
Citation: I. V. Frolenkov, E. N. Kriger, “On the solvability of the Cauchy problem for a certain class of multidimensional loaded parabolic equations”, Mathematical Analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 156, VINITI, Moscow, 2018, 41–57; J. Math. Sci. (N. Y.), 254:6 (2021), 743–760
Citation in format AMSBIB
\Bibitem{FroKri18}
\by I.~V.~Frolenkov, E.~N.~Kriger
\paper On the solvability of the Cauchy problem for a certain class of multidimensional loaded parabolic equations
\inbook Mathematical Analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 156
\pages 41--57
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into396}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3939195}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 254
\issue 6
\pages 743--760
\crossref{https://doi.org/10.1007/s10958-021-05337-y}
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