Geodesic
A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 2, pp. 225-235

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In the cylindrical domain of Euclidean space for one class of multidimensional hyperbolic parabolic equations the spectral Dirichlet problem with homogeneous boundary conditions is considered. The solution is sought in the form of an expansion in multidimensional spherical functions. The existence and uniqueness theorems of the solution are proved. Conditions for the unique solvability of the problem are obtained, which essentially depend on the height of the cylinder.
Keywords: multidimensional hyperbolic-parabolic equation, Dirichlet spectral problem, multidimensional cylindrical domain. 
@article{VSGTU_2018_22_2_a2,
     author = {S. A. Aldashev},
     title = {A criterion for the unique solvability of the spectral {Dirichlet} problem for a class of multidimensional hyperbolic-parabolic equations},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {225--235},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2018_22_2_a2/}
}
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S. A. Aldashev. A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 2, pp. 225-235. http://geodesic.mathdoc.fr/item/VSGTU_2018_22_2_a2/