Andreev, Aleksandr Anatol’evich; Yakovleva, Yuliya Olegovna The Goursat-type problem for a hyperbolic equation and system of third order hyperbolic equations. (Russian. English summary) Zbl 1438.74034 Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 23, No. 1, 186-194 (2019). Summary: In the first part of this study, the well-posed Goursat-type problem is considered for the hyperbolic differential equation of the third order with non-multiple characteristics. The example illustrating the non-well-posed Goursat-type problem for the hyperbolic differential equation of the third order is discussed. The regular solution of the Goursat-type problem for the hyperbolic differential equation of the third order with the non-multiple characteristics is obtained in an explicit form.In the second part, the well-posed Goursat-type problem is considered for a system of the hyperbolic differential equations of the third order. The regular solution of the Goursat-type problem for this system is also obtained in an explicit form.The theorems for the Hadamard’s well-posedness of Goursat-type problem for the hyperbolic differential equation and for a system of the hyperbolic differential equations is formulated as the result of the research. MSC: 74E35 Random structure in solid mechanics 74K20 Plates Keywords:third-order hyperbolic equation; non-multiple characteristics; Goursat-type problem; hyperbolic system of third-order differential equations; Hadamard correctness × Cite Format Result Cite Review PDF Full Text: DOI MNR References: [1] Muskhelishvili N. I., Nekotorye osnovnye zadachi matematicheskoi teorii uprugosti. Osnovnye uravneniia, ploskaia teoriia uprugosti, kruchenie i izgib [Some basic problems of the mathematical theory of elasticity. Fundamental equations, plane theory of elasticity, torsion and bending], Nauka, Moscow, 1966, 707 pp. (In Russian) · Zbl 0151.36201 [2] Hadamard J., Lectures on Cauchy’s problem in linear partial differential equations, Dover Publications, New York, 1952, v+316 pp. · Zbl 0049.34805 [3] Bitsadze A. V., “On the question of formulating the characteristic problem for second order hyperbolic systems”, Dokl. Akad. Nauk SSSR, 223:6 (1975), 1289-1292 (In Russian) · Zbl 0333.35050 [4] Dzhokhadze O. M., “Influence of lower terms on the well-posedness of characteristics problems for third-order hyperbolic equations”, Math. Notes, 74:4 (2003), 491-501 · Zbl 1082.35094 · doi:10.1023/A:1026139709809 [5] Kharibegashvili S. S., “Solvability of a characteristic problem for second-order degenerate hyperbolic systems”, Differ. Equ., 25:1 (1989), 123-131 · Zbl 0695.35129 [6] Zikirov O. S., “On solvability non-local boundary value problem for the hyperbolic equation of the third order”, Sib. J. Pure and Appl. Math., 16:2 (2016), 16-25 (In Russian) · Zbl 1399.35267 · doi:10.17377/PAM.2016.16.202 [7] Kinoshita T., “Gevrey wellposedness of the Cauchy problem for the hyperbolic equations of third order with coefficients depending only on time”, Publications of the Research Institute for Mathematical Sciences, 34:3, 249-270 · Zbl 0973.35138 · doi:10.2977/prims/1195144695 [8] Nikolov A., Popivanov N., “Singular solutions to Protter‘s problem for (3+1)-D degenerate wave equation”, AIP Conf. Proc., 1497 (2012), 233-238 · doi:10.1063/1.4766790 [9] Colton D., “Pseudoparabolic equations in one space variable”, J. Differ. Equ., 12:3 (1972), 559-565 · Zbl 0231.35038 · doi:10.1016/0022-0396(72)90025-3 [10] Andreev A. A., Yakovleva J. O., “The characteristic problem for one hyperbolic differentional equation of the third order with nonmultiple characteristics”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 13:1(2) (2013), 3-6 (In Russian) · Zbl 1293.35164 [11] Korzyuk V. I., Cheb E. S., Thu L. T., “Solution of the mixed problem for the biwave equation by the method of characteristics”, Tr. Inst. Mat., 18:2 (2010), 36-54 (In Russian) · Zbl 1219.35135 [12] Petrovskii I. G., Izbrannye trudy. Sistemy uravnenii s chastnymi proizvodnymi. Algebraicheskaya geometriya, Nauka, M., 1986, 504 pp. · Zbl 0603.01018 [13] Yakovleva J. O., “One characteristic problem for the general hyperbolic differential equation of the third order with nonmultiple characteristics”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, no. 3(28), 180-183 (In Russian) · Zbl 1326.35181 · doi:10.14498/vsgtu1108 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.