Geodesic
The Cauchy problem for a general hyperbolic differential equation of the $n$-th order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 2, pp. 241-248

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In the paper the problem of Cauchy is considered for the hyperbolic differential equation of the $n$-th order with the nonmultiple characteristics. The Cauchy problem is considered for the hyperbolic differential equation of the third order with the nonmultiple characteristics for example. The analogue of D'Alembert formula is obtained as a solution of the Cauchy problem for the hyperbolic differential equation of the third order with the nonmultiple characteristics. The regular solution of the Cauchy problem for the hyperbolic differential equation of the forth order with the nonmultiple characteristics is constructed in an explicit form. The regular solution of the Cauchy problem for the $n$-th order hyperbolic differential equation with the nonmultiple characteristics is constructed in an explicit form. The analogue of D'Alembert formula is obtained as a solution of this problem also. The existence and uniqueness theorem for the regular solution of the Cauchy problem for the $n$-th order hyperbolic differential equation with the nonmultiple characteristics is formulated as the result of the research.
Keywords: $n$-th order hyperbolic differential equation, nonmultiple characteristics, Cauchy problem
Mots-clés : D'Alembert formula. 
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     author = {A. A. Andreev and J. O. Yakovleva},
     title = {The {Cauchy} problem for a general hyperbolic differential equation of the $n$-th order},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {241--248},
     publisher = {mathdoc},
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     year = {2016},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2016_20_2_a2/}
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A. A. Andreev; J. O. Yakovleva. The Cauchy problem for a general hyperbolic differential equation of the $n$-th order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 2, pp. 241-248. http://geodesic.mathdoc.fr/item/VSGTU_2016_20_2_a2/