Nonlocal Inverse Problem of Finding Unknown Multipliers in the Right-Hand Part of Lavrentiev-Bitsadze Equation

Abstract

We consider an equation of mixed elliptic-hyperbolic type. The right-hand part of the equation is represented as a product of two functions, each which only depends on one of variables. We study an inverse problem for this equation; it consists in finding the unknown multipliers. We establish a uniqueness criterion for this problem. The solution is constructed as a series in eigenfunctions for the corresponding one-dimensional spectral problem. Under some conditions on the boundary of domain, boundary values, and the unknown multipliers, we establish separation from zero of small denominators of ratios containing in the coefficients of the series; the existence of solution and its stability are proved as well.