Abstract:
We study a one-dimensional system of two parabolic loaded equations of special kind and one-dimensional composite-type systems of special kind. Both systems are considered with Cauchy data. We obtain sufficient conditions for the existence of solutions in the class of smooth bounded functions. The method of splitting on the differential level (the weak approximation method) is used in the proof.
Keywords:
inverse problem, direct problem, loaded equation, parabolic equation, weak approximation method, system of partial differential equations, composite-type system.
Citation:
I. V. Frolenkov, G. V. Romanenko, “On the solvability of special systems of one-dimensional loaded parabolic equations and composite-type systems with Cauchy data”, Sib. Zh. Ind. Mat., 17:1 (2014), 135–148; J. Appl. Industr. Math., 8:2 (2014), 196–207
\Bibitem{FroRom14}
\by I.~V.~Frolenkov, G.~V.~Romanenko
\paper On the solvability of special systems of one-dimensional loaded parabolic equations and composite-type systems with Cauchy data
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 1
\pages 135--148
\mathnet{http://mi.mathnet.ru/sjim826}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3379261}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 2
\pages 196--207
\crossref{https://doi.org/10.1134/S1990478914020069}
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https://www.mathnet.ru/eng/sjim826
https://www.mathnet.ru/eng/sjim/v17/i1/p135
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