The Dirichlet problem for a mixed-type equation with characteristic degeneration in a rectangular domain

Аннотация

We study the first boundary-value problem for the following mixed-type equation of the second kind: $$ u_{xx} + yu_{yy} + au_y - b^2 u = 0 $$ in the domain {(x, y) | 0 < x < 1, −α < y < β}, where a, b, α, and β are given real numbers, and 0 < a < 1, b ≥ 0, α > 0, β > 0. Based on the completeness of the system of eigenfunctions of one-dimensional spectral problem we establish a uniqueness criterion. We construct a solution to the problem as the sum of the series in eigenfunctions.

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DOI

10.3103/s1066369x0911005x

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