Abstract:
We consider the Dirichlet problem for linear hyperbolic equations of the third order. We prove the existence and uniqueness of classical solution with the use of an energy inequality and Riemann's method. We reveal the effect of influence of coefficients at minor derivatives on the well-posedness of the Dirichlet problem.
Citation:
O. S. Zikirov, “On the Dirichlet problem for hyperbolic equations of the third order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 7, 63–71; Russian Math. (Iz. VUZ), 58:7 (2013), 53–60
\Bibitem{Zik14}
\by O.~S.~Zikirov
\paper On the Dirichlet problem for hyperbolic equations of the third order
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 7
\pages 63--71
\mathnet{http://mi.mathnet.ru/ivm8912}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 58
\issue 7
\pages 53--60
\crossref{https://doi.org/10.3103/S1066369X14070068}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84903707647}
Linking options:
https://www.mathnet.ru/eng/ivm8912
https://www.mathnet.ru/eng/ivm/y2014/i7/p63
This publication is cited in the following 11 articles:
A. A. Matchanova, “Inverse Problem for a Third-Order Parabolic-Hyperbolic Equation Involves Fractional Derivatives”, Lobachevskii J Math, 44:3 (2023), 1197
Yu. P. Apakov, A. A. Hamitov, “On solution of the boundary value problems posed for an equation with the third-order multiple characteristics in semi-bounded domains in three dimensional space”, Bol. Soc. Mat. Mex., 29:3 (2023)
Yu. P. Apakov, A. A. Hamitov, “Third Boundary Value Problem for an Equation with the Third Order Multiple Characteristics in Three Dimensional Space”, Lobachevskii J Math, 44:2 (2023), 523
T. K. Yuldashev, “Mixed problem for pseudoparabolic integro-differential equation with degenerate kernel”, Differ. Equ., 53:1 (2017), 99–108
T. K. Yuldashev, “Nelokalnaya kraevaya zadacha dlya neodnorodnogo psevdoparabolicheskogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 42–54
T. K. Yuldashev, “Nelineinoe integro-differentsialnoe uravnenie psevdoparabolicheskogo tipa s nelokalnym integralnym usloviem”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 1(32), 11–23
T. K. Yuldashev, “Obratnaya zadacha dlya integro-differentsialnogo uravneniya Fredgolma tretego poryadka s vyrozhdennym yadrom”, Vladikavk. matem. zhurn., 18:2 (2016), 76–85
T. K. Yuldashev, “Smeshannoe differentsialnoe uravnenie tipa Bussineska”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 2(33), 13–26
T. K. Yuldashev, “Nonlocal problem for a mixed type differential equation in rectangular domain”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 3, 70–78
T. K. Yuldashev, K. Kh. Shabadikov, “Kvazilineinoe integro-differentsialnoe uravnenie psevdoparabolicheskogo tipa s vyrozhdennym yadrom i integralnym usloviem”, Zhurnal SVMO, 18:4 (2016), 76–88
T. K. Yuldashev, “On Fredholm partial integro-differential equation of the third order”, Russian Math. (Iz. VUZ), 59:9 (2015), 62–66
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