Determining a Source Function in the Mixed Parabolic–Hyperbolic Equation with Characteristic Type Change Line

In this paper, we study the direct and inverse problems for a model equation of a mixed parabolic-hyperbolic type. In the direct problem, an analog of the Tricomi problem for this equation with a characteristic line of type change is considered. The unknown of the inverse problem is the y-dependent source function of the parabolic equation. To determine it with respect to the solution defined in the parabolic part of the domain, an overdetermination at the point $$x=x_{0}$$ for $$y>0$$ condition is specified. Local theorems on the unique solvability of the problems posed in the sense of the classical solution are proved.

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