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- W2074161463 abstract "IT is shown that Vladimirov's boundary conditions are dissipatively minimal in the P2n + 1-approximation of the method of spherical harmonics. Similar conditions are proposed for P2n. For a symmetric hyperbolic system obtained from the one-velocity kinetic equation in the P2n + 1-approximation of the method of spherical harmonics, it is shown that Vladimirov's boundary conditions are the dissipatively minimal boundary conditions. Similar conditions are proposed for the P2n-approximation. The proof is based on the polynomial inequalities established in section 1. In order to use these boundary conditions in practical calculations, in section 3 we have given the matrices of these conditions for a boundary surface with an arbitrarily oriented normal. In section 4 we have also derived the equations of the method of spherical harmonics in arbitrary orthogonal curvilinear coordinates. The use of these coordinates considerably facilitates the writing out of the boundary conditions and makes it possible to dispense with generalized spherical functions in formulating them." @default.
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- W2074161463 date "1971-01-01" @default.
- W2074161463 modified "2023-09-25" @default.
- W2074161463 title "The dissipativity of Vladimirov's boundary conditions for a symmetric system of the method of spherical harmonics" @default.
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- W2074161463 doi "https://doi.org/10.1016/0041-5553(71)90138-8" @default.
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