Boundary Value Problems for a Parabolic-Hyperbolic Equation with a Superposition of Operators of the First and Second Orders
B. I. IslomovNational University of Uzbekistan, 100174, Tashkent, UzbekistanT. K. YuldashevTashkent State University of Economics, 100066, Tashkent, UzbekistanG. K. KylyshbayevaNational University of Uzbekistan, 100174, Tashkent, Uzbekistan
ABI
Abstract
The paper proposes a method for solving the problem for a parabolic-hyperbolic equation of the third order in a rectangular domain, when the main part of equation contains a first-order operator. A criterion for the uniqueness of the solution is established. When justifying the uniform convergence of the Fourier series, the problem of small denominators arises. In this regard, estimates of small denominators about the distance from zero with the corresponding asymptotics are established. These estimates made it possible to prove the convergence of the series in the class of regular solutions of this equation. Estimates on the stability of the solution from given boundary functions are proved.
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