Dirichlet Problem for Mixed Type Equation with Characteristic Degeneration and Singular Coefficient

Abstract

Listen

Translate article

For a mixed-type equation of the second kind with a singular coefficient by the spectral expansions uniqueness criterion is installed for solving the first boundary-value problem. The solution was constructed as the sum of a Fourier–Bessel series. In justifying the uniform convergence appeared the problem of small denominators. In connection with this evaluation is set on a small separation from zero denominator with the corresponding asymptotic behavior that allowed to justify the convergence of the series in the class of regular solutions.