We study nonlinear inverse problems for first order hyperbolic equations. We find a solution and an unknown coefficient depending on the time variable. For additional conditions we consider integral and boundary overdetermination conditions. We establish the existence of a regular solution, i.e., the solution possesses all generalized derivatives in the sense of Sobolev entering the equation.
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Kozhanov, A., Zhalgassova, K.A. Nonlinear Inverse Problems for First Order Hyperbolic Equations. J Math Sci 281, 857–867 (2024). https://doi.org/10.1007/s10958-024-07155-4
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DOI: https://doi.org/10.1007/s10958-024-07155-4