Bukhara branch of the Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Bukhara State University, 11 M. Ikbol str., Bukhara, 200118 Republic of Uzbekistan
Abstract:
The direct and inverse problems for a model mixed parabolic-hyperbolic equation with a characteristic line of type change have been studied. In the direct problem, a nonlocal problem for this equation with interior boundary conditions in the hyperbolic part of the domain has been investigated. The unknown of the inverse problem is the variable coefficient of the lower-order term in the parabolic equation. To determine it, the inverse problem is studied under the assumption that an integral overdetermination condition is known for the solution defined in the parabolic part of the domain. A theorem of unique solvability for the posed problems in the sense of a classical solution has been proven.
Keywords:equation of mixed parabolic-hyperbolic type, direct problem, inverse problem, existence, uniqueness, integral equation, contraction mapping principle.
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