Abstract:
We consider problems with the Bitsadze–Samarskii-type conditions for a mixed parabolic-hyperbolic equation with noncharacteristic type change curve. We prove theorems on the unique existence of regular and strong solutions and the Volterra property for the problems under consideration.
Citation:
A. S. Berdyshev, “The volterra property of some problems with the Bitsadze–Samarskii-type conditions for a mixed parabolic-hyperbolic equation”, Sibirsk. Mat. Zh., 46:3 (2005), 500–510; Siberian Math. J., 46:3 (2005), 386–395
\Bibitem{Ber05}
\by A.~S.~Berdyshev
\paper The volterra property of some problems with the Bitsadze--Samarskii-type conditions for a~mixed parabolic-hyperbolic equation
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 3
\pages 500--510
\mathnet{http://mi.mathnet.ru/smj982}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2164555}
\zmath{https://zbmath.org/?q=an:1094.35084}
\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 3
\pages 386--395
\crossref{https://doi.org/10.1007/s11202-005-0041-y}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000229958200002}
Linking options:
https://www.mathnet.ru/eng/smj982
https://www.mathnet.ru/eng/smj/v46/i3/p500
This publication is cited in the following 12 articles:
Maksat Ashyraliyev, Maral Ashyralyyeva, “Stable difference schemes for hyperbolic–parabolic equations with unknown parameter”, Bol. Soc. Mat. Mex., 30:1 (2024)
Nauryzbay Adil, Abdumauvlen S. Berdyshev, B. E. Eshmatov, Zharasbek D. Baishemirov, “Solvability and Volterra property of nonlocal problems for mixed fractional-order diffusion-wave equation”, Bound Value Probl, 2023:1 (2023)
Sadybekov M.A., Dildabek G., Ivanova M.B., “Spectral Properties of a Frankl Type Problem For Parabolic-Hyperbolic Equations”, Electron. J. Differ. Equ., 2018
Dildabek G., Sadybekov M.A., Saprygina M.B., “On a Volterra Property of An Problem of the Frankl Type For An Equation of the Mixed Parabolic-Hyperbolic Type”, Proceedings of the 43rd International Conference Applications of Mathematics in Engineering and Economics, AMEE'17, AIP Conference Proceedings, 1910, eds. Pasheva V., Popivanov N., Venkov G., Amer. Inst. Physics, 2017, UNSP 040004
Dildabek G., Saprygina M.B., “Volterra Property of An Problem of the Frankl Type For An Parabolic-Hyperbolic Equation”, International Conference Functional Analysis in Interdisciplinary Applications (FAIA 2017), AIP Conference Proceedings, 1880, eds. Kalmenov T., Sadybekov M., Amer. Inst. Physics, 2017, UNSP 050011
T. Sh. Kal'menov, M. A. Sadybekov, “On a Frankl-type problem for a mixed parabolic-hyperbolic equation”, Siberian Math. J., 58:2 (2017), 227–231
Dildabek G., “on a New Nonlocal Boundary Value Problem For An Equation of the Mixed Parabolic-Hyperbolic Type”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conference Proceedings, 1789, eds. Pasheva V., Popivanov N., Venkov G., Amer Inst Physics, 2016, UNSP 040018
Kalmenov T.Sh., Sadybekov M., “on a Problem of the Frankl Type For An Equation of the Mixed Parabolic-Hyperbolic Type”, International Conference on Analysis and Applied Mathematics (ICAAM 2016), AIP Conference Proceedings, 1759, eds. Ashyralyev A., Lukashov A., Amer. Inst. Physics, 2016, 020001
Abdumauvlen S Berdyshev, Alberto Cabada, Erkinjon T Karimov, Nazgul S Akhtaeva, “On the Volterra property of a boundary problem with integral gluing condition for a mixed parabolic-hyperbolic equation”, Bound Value Probl, 2013:1 (2013)
He Ch., Liu Ch., “Nonexistence for mixed-type equations with critical exponent nonlinearity in a ball”, Appl. Math. Lett., 24:5 (2011), 679–686
Berdyshev A.S., Rakhmatullaeva N.A., “Non-Local Problems for Parabolic-Hyperbolic Equations with Deviation From the Characteristics and Three Type-Changing Lines”, Electronic Journal of Differential Equations, 2011, 07
Babak P., “Nonlocal problems involving spatial structure for coupled reaction-diffusion systems”, Applied Mathematics and Computation, 185:1 (2007), 449–463
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