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Tricomi problem for \(q\)-difference analog of anticipatory-retarding equation of mixed type. (English. Russian original) Zbl 1383.35133

Russ. Math. 61, No. 1, 1-9 (2017); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2017, No. 1, 3-11 (2017).
Summary: We investigate a boundary-value problem for mixed-type equation with the Lavrent’ev-Bitsadze operator in the main term and \(q\)-difference deviations of the argument in the lowest terms. We construct a general solution to the equation and prove a uniqueness theorem without restrictions on the deviation value. Then we show that the problem is uniquely solvable and find integral representations of the solution in the elliptic and hyperbolic domains.

MSC:

35M12 Boundary value problems for PDEs of mixed type
35C15 Integral representations of solutions to PDEs
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