Geodesic
On some class of the pseudohyperbolic equations with an unknown coefficient
Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 2, pp. 164-180

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We consider the inverse problems with an unknown coefficient $a$ for a pseudohyperbolic equation $u_{tt}-\Delta u-\Delta u_{tt}+au=f(x,t)$ and investigate the solvability of the problem. We prove the theorems of the existence of the problem's regular solutions. The distinctiveness of the problems is a presence of new overdetermination conditions for the considered class of equations.
Keywords: pseudohyperbolic equation, unknown coefficient, inverse problem, integral overdetermination, regular solution, existence. 
@article{CHFMJ_2022_7_2_a3,
     author = {A. I. Kozhanov and R. R. Safiullova},
     title = {On some class of the pseudohyperbolic equations with an unknown coefficient},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {164--180},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_2_a3/}
}
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A. I. Kozhanov; R. R. Safiullova. On some class of the pseudohyperbolic equations with an unknown coefficient. Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 2, pp. 164-180. http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_2_a3/