Inverse Problem of Determining Two Coefficients of Lower-Order Terms in a Mixed Parabolic-Hyperbolic Equation

Abstract

Direct and inverse problems for a model equation of mixed parabolic-hyperbolic type are studied. In the direct problem, we consider a Tricomi-type problem for this equation with a noncharacteristic line of type change. The unknowns of the inverse problem are the variable coefficients of the lower-order terms in the equation. To determine these coefficients, an integral overdetermination condition is specified relative to the solution defined in the parabolic part of the domain, and in the hyperbolic part, conditions are specified on the characteristics: on one characteristic it is the value of the normal derivative and on the other, the value of the function itself. Theorems for the unique solvability of the posed problems in the sense of classical solution are proved.