Inner boundary value problem with displacement for a second order mixed parabolic-hyperbolic equation
DOI:
https://doi.org/10.31489/2022m2/59-71Keywords:
wave equation, degenerate hyperbolic equation of the first kind, Volterra integral equation, Fredholm integral equation, Tricomi method, method of integral equations, methods of fractional calculus theoryAbstract
This paper investigates inner boundary value problems with a shift for a second-order mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic operator of the first kind in the other part. We find sufficient conditions for the given functions to ensure the existence of a unique regular solution to the problems under study. In some special cases, solutions are obtained explicitly.
