Geodesic
A~method for solution of a~mixed boundary value problem for a~hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$
Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1227-1254

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A mixed boundary value problem with arbitrary continuous, not necessarily satisfying boundary conditions, functions in initial conditions and inhomogeneities of the equation is solved. A method is proposed for finding a generalized solution by a modification of the interpolation operators of functions constructed from solutions of Cauchy problems with second-order differential expression. Methods of finding the Fourier coefficients of auxiliary functions using the Stieltjes integral or the resolvent of the third-order Cauchy differential operator are proposed.
Keywords: boundary value problem, generalized solution, method of separation of variables. 
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     author = {A. Yu. Trynin},
     title = {A~method for solution of a~mixed boundary value problem for a~hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$},
     journal = {Izvestiya. Mathematics },
     pages = {1227--1254},
     publisher = {mathdoc},
     volume = {87},
     number = {6},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a5/}
}
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A. Yu. Trynin. A~method for solution of a~mixed boundary value problem for a~hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$. Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1227-1254. http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a5/