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

Direct and inverse problems for a model equation of mixed parabolic-hyperbolic type arestudied. In the direct problem, we consider a Tricomi-type problem for this equation with anoncharacteristic line of type change. The unknowns of the inverse problem are the variablecoefficients of the lower-order terms in the equation. To determine these coefficients, an integraloverdetermination condition is specified relative to the solution defined in the parabolic part of thedomain, and in the hyperbolic part, conditions are specified on the characteristics: on onecharacteristic it is the value of the normal derivative and on the other, the value of the functionitself. Theorems for the unique solvability of the posed problems in the sense of classical solutionare proved.