BOUNDARY VALUE PROBLEM FOR LOADED THIRD-ORDER PARABOLIC-HYPERBOLIC EQUATION IN AN INFINITE THREE DIMENSIONAL DOMAIN
DOI:
https://doi.org/10.52754/16948645_2023_1_59Keywords:
Key words:. Third-order equation, loaded equation, Gellerstedt problem, Fourier transform, regular solution, extremum principle, estimation of the solution.Abstract
In this paper, we formulate and study the problem with Gellerstedt conditions on different characteristic planes for a loaded parabolic-hyperbolic equation of the third order in a three-dimensional domain. The main method of the study of the problem is the Fourier transform. Based on the Fourier transform, the problem and equation are reduced to a planar analogue of the Gellerstedt problem with a spectral parameter, both in the equation and in boundary conditions.
The uniqueness of the solution of the problem is proved using a new extremum principle for loaded equations of mixed type of the third order. Using a general representation of the solution, the existence of a solution to the problem by the method of integral equations is proved. In addition, the asymptotic behavior of the solution of the problem for large values of the spectral parameter is studied. Sufficient conditions have been found under which all operations are legal.
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Islomov B.I., Alikulov Y.K. Boundary value problem for loaded equation of parabolic-giperbolic type of the third order in an infinite three-dimensional domain //International journal of applied mathematics, 2021, Vol.34, No.2, pp.158-170, DOI: https://doi.org/10.12732/ijam.v34i2.13
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