Abstract:
The paper investigates a nonlocal problem with a shift to the conjugation of model equations of parabolic and hyperbolic types of the second order, consisting of a heat equation in the parabolic part of the mixed domain and a degenerate hyperbolic equation of the first kind in the other part. Using an analogue of the Tricomi method and known properties of the theory of fractional calculus, sufficient conditions for given functions are found to ensure the existence of a unique solution to the problem under study that is regular in the domain under consideration. In one particular case, the solution to the problem is written out explicitly.
Keywords:mixed type equation, heat equation, degenerate hyperbolic equation, fractional calculus, Volterra equation, Tricomi method, method of integral equations
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