Geodesic
On the Dirichlet problem for hyperbolic equations of the third order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 63-71

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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.
Keywords: hyperbolic equation, boundary-value problem, Dirichlet problem, Riemann's function, Fredholm and Volterra equations.
Mots-clés : Goursat problem 
@article{IVM_2014_7_a5,
     author = {O. S. Zikirov},
     title = {On the {Dirichlet} problem for hyperbolic equations of the third order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {63--71},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_7_a5/}
}
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O. S. Zikirov. On the Dirichlet problem for hyperbolic equations of the third order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 63-71. http://geodesic.mathdoc.fr/item/IVM_2014_7_a5/