Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University645010.18287/2541-7525-2018-24-3-30-34UnknownTHE CAUCHY PROBLEM FOR THE HYPERBOLIC DIFFERENTIAL EQUATION OF THE THIRD ORDERYakovlevaJ. O.morenov@ssau.ruSamara State Technical Universuty1111201824330341101201911012019Copyright © 2018, Yakovleva J.O.2018<p>In the article the Cauchy problem for the third order hyperbolic differential equation with nonmultiple characteristics is considered on the plane of two independent variables. The differential equation has tree nonmultiple characteristics and this equation is strongly hyperbolic equation. The regular solution of the Cauchy problem for the hyperbolic differential equation of the third order with the nonmultiple characteristics is constructed in an explicit form, the solution is obtained by the method of general solutions. The solution of the Cauchy problem enables describing the propagation of initial displacement, initial velocity and initial acceleration.</p>дифференциальное уравнение третьего порядка, гиперболическое уравнение, некратные характеристики, метод общих решений, задача Коши, регулярное решение, начальное отклонение, начальная скорость.differential equation of the third order, hyperbolic equation of the third order, nonmultiple characteristics, method of common solutions, Cauchy problem, regular solution, initial displacement, initial velocity. Korzyuk V.I., Cheb E.S., Le Thi Thu. Reshenie smeshannoi zadachi dlia bivolnovogo uravneniia metodom kharakteristik [Solution of the mixed problem for the biwave equation by the method of characteristics]. Tr. Inta matem. [Trudy Instituta Matematiki], 2010, no. 2(18), pp. 36–54. Available at: <a href='http://mi.mathnet.ru/timb16'>http://mi.mathnet.ru/timb16</a> [in Russian]. Petrovskiy I.G. Izbrannye trudy. Sistemy uravnenii s chastnymi proizvodnymi. Algebraicheskaia geometriia [Selected works. Systems of partial differential equations. Algebraic geometry]. M.: Nauka, 1986, 500 p. [in Russian]. Andreev A.A., Yakovleva Ju.O. Zadacha Koshi dlia sistemy uravnenii giperbolicheskogo tipa chetvertogo poriadka obshchego vida s nekratnymi kharakteristikami [Cauchy Problem For the System of General HyperbolicDifferential Equations of the Forth Order with Nonmultiple Characteristics]. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Seriia fiz. mat. nauki [Journal of Samara State Technical University. Ser. Physical and Mathematical Sciences], 2014, Vol. 37, no. 4, pp. 7–15. DOI: https://doi.org/<a href='http://doi.org/10.14498/vsgtu1349'>10.14498/vsgtu1349</a> [in Russian]. Andreev A.A., Yakovleva Ju.O. Zadacha Koshi dlia sistemy differentsial’nykh uravnenii giperbolicheskogo tipa poriadka n s nekratnymi kharakteristikami [The Cauchy problem for a general hyperbolic differential equation of the n-th order with the nonmultiple characteristics]. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Seriia fiz.-mat. nauki [Journal of Samara State Technical University. Ser. Physical and Mathematical Sciences], 2017, Vol. 21, no. 4, pp. 752–759. DOI: https://doi.org/<a href='http://doi.org/10.14498/vsgtu1577'>10.14498/vsgtu1577</a> [in Russian]. Yakovleva Ju.O. [The analogue of D’Alembert formula for hyperbolic differential equation of the third order with nonmultiple characteristics]. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Seriia fiz.-mat. nauki [Journal of Samara State Technical University. Ser. Physical and Mathematical Sciences], 2012, Vol. 26, no. 1, pp. 247–250. DOI: https://doi.org/10.14498/vsgtu1028 [in Russian]. Tikhonov A.N., Samarskii A.A. Uravneniia matematicheskoi fiziki [Equations of mathematical physics]. M.: Izd-vo Nauka, 1972, 735 p. [in Russian].