Determination of the coefficient function in a Whitham type nonlinear differential equation with impulse effects
https://doi.org/10.17586/2220-8054-2023-14-3-312-320
Abstract
In the article, the problems of unique solvability and determination of the redefinition coefficient function in the initial inverse problem for a nonlinear Whitham type partial differential equation with impulse effects are studied. The modified method of characteristics allows partial differential equations of the first order to be represented as ordinary differential equations that describe the change of unknown function along the line of characteristics. The unique solvability of the initial inverse problem is proved by the method of successive approximations and contraction mappings. The determination of the unknown coefficient is reduced to solving the nonlinear integral equation.
Keywords
inverse problem,
Whitham type equations,
determination of the coefficient function,
method of successive approximations,
unique solvability
Supporting agencies: The research of the first author is funded by the Ministry of Innovative development of the Republic of Uzbekistan (Grant F-FA-2021-424).
About the Authors
T. K. Yuldashev
Tashkent State University of Economics
Uzbekistan
Uzbekistan
Tursun K. Yuldashev
Karimov street, 49, TSUE, Tashkent, 100066
A. K. Fayziyev
Tashkent State University of Economics
Uzbekistan
Uzbekistan
Aziz K. Fayziyev
Karimov street, 49, TSUE, Tashkent, 100066
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Review
For citations:
Yuldashev T.K., Fayziyev A.K. Determination of the coefficient function in a Whitham type nonlinear differential equation with impulse effects. Nanosystems: Physics, Chemistry, Mathematics. 2023;14(3):312-320. https://doi.org/10.17586/2220-8054-2023-14-3-312-320
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