Inverse Problem for Degenerate Parabolic-Hyperbolic Equation with Nonlocal Boundary Condition

摘要

For a mixed type equation with a power-law degeneration we consider the inverse problem on finding an unknown right side. We establish a uniqueness criterion of solution to the problem with a nonlocal condition that connects the normal derivative of the sought-for solution, which belongs to different types of studied equations. The solution is constructed in the form of sums of a series in eigenfunctions of the corresponding one-dimensional spectral problem. We also prove stability of the solution to the nonlocal boundary condition.