Geodesic
Characteristic problem for a fourth-order equation with a dominant derivative
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 3, pp. 14-21

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In this article we consider the Goursat problem for an equation with a dominating fourth-order mixed derivative and prove its unique solvability. The equation under consideration can be interpreted as a generalized Boussinesq — Love equation, which arises when describing longitudinal waves in a rod, taking into account transverse deformations. To justify the solvability, we proposed a method that is based on the possibility of reducing the problem posed to two Goursat problems for second-order equations. One of the problems is the classical Goursat problem for the simplest hyperbolic equation, while the other equation is loaded, and the study of the Goursat problem for it is the main result of the work.
Mots-clés : Boussinesq — Love equation, Goursat problem, existence of a solution
Keywords: system of two problems, equation with dominant derivative, loaded equation, method of successive approximations, uniqueness of a solution. 
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     title = {Characteristic problem for a fourth-order equation with a dominant derivative},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
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     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2021_27_3_a1/}
}
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A. V. Gilev; O. M. Kechina; L. S. Pulkina. Characteristic problem for a fourth-order equation with a dominant derivative. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 3, pp. 14-21. http://geodesic.mathdoc.fr/item/VSGU_2021_27_3_a1/