Determining a Source Function in the Mixed Parabolic–Hyperbolic Equation with Characteristic Type Change Line
D. K. DurdievBukhara Branch of the Romanovskiy Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan, 200100, Bukhara, UzbekistanD. A. ToshevBukhara Branch of the Romanovskiy Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan, 200100, Bukhara, UzbekistanH. H. TurdievBukhara Branch of the Romanovskiy Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan, 200100, Bukhara, Uzbekistan
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Аннотация
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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