Geodesic
Coefficient inverse problem for Whitham type two-dimensional differential equation with impulse effects
Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 2, pp. 238-248

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In the article the questions of unique solvability and determination of the redefinition coefficient function in the initial inverse problem for two-dimensional 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 an unknown function along the line of characteristics. The unique solvability of the two-dimensional inverse problem is proved by the method of successive approximations and contraction mappings. The definition of the unknown coefficient is reduced to solving the Volterra integral equation of the first kind.
Keywords: inverse problem, two-dimensional Whitham type equation, determination of the coefficient function, method of successive approximations, unique solvability. 
@article{CHFMJ_2023_8_2_a6,
     author = {T. K. Yuldashev and T. G. Ergashev and A. K. Fayziyev},
     title = {Coefficient inverse problem for {Whitham} type two-dimensional differential equation with impulse effects},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {238--248},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_2_a6/}
}
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T. K. Yuldashev; T. G. Ergashev; A. K. Fayziyev. Coefficient inverse problem for Whitham type two-dimensional differential equation with impulse effects. Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 2, pp. 238-248. http://geodesic.mathdoc.fr/item/CHFMJ_2023_8_2_a6/