EQUATIONS
Print ISSN: , E-ISSN: 2944-9146 An Open Access International Journal of Mathematical and Computational Methods in Science and Engineering
Volume 3, 2023
On the Correction Method of Test Solutions to the New Model Wave Equation with Two Variable Rates in First Quarter of the Plane
Author: Fedor Egorovich Lomovtsev
Abstract: A correction method of test solutions into classical solutions to a new inhomogeneous model wave
equation with variable two-rates in the first quarter of the plane was developed to derive the minimum
smoothness requirement of its right-hand side. In the case of different rates, it is not possible to derive the
minimum smoothness of right-hand side of the inhomogeneous model wave equation in the first quarter of the
plane without correcting both test generalized and test classical solutions. In this paper, classical solutions to
the inhomogeneous two-rate model wave equation and the smoothness criterion of their right-hand side are
obtained. We need them to find explicit unique and stable classical solutions and Hadamard correctness criteria
to mixed (initial-boundary) problems for this wave equation using developed by the author of the ”implicit
characteristics method”.
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Keywords: Two-rate model wave equation, correction method, test solution, classical solution, implicit
characteristics method, smoothness criterion, correctness criterion
Pages: 41-43
DOI: 10.37394/232021.2023.3.5
Equations, ISSN / E-ISSN: / 2944-9146, Volume 3, 2023, Art. #5