We consider the inverse problem for a quasilinear second order elliptic equation with the unknown coefficient at the lower-order term and the first kind boundary condition and the integral overedetermination condition on the boundary. We prove a theorem on the local existence and uniqueness of a strong solution to the problem. The result is illustrated by an example of a nonlinear equation satisfying all the assumptions of the theorem.
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A. Sh. Lyubanova, “Identification of a constant coefficient in an elliptic equation,” Appl. Anal. 87, No. 10-11, 1121–1128 (2008).
A. Sh. Lyubanova and A. Tani, “An inverse problem for pseudoparabolic equation of filtration: the existence, uniqueness and regularity,” Appl. Anal. 90, No. 10, 1557–1571 (2011).
A. Sh. Lyubanova, “Inverse problems for nonlinear stationary equations,” Mat. Zamet. SVFU 23, No. 2, 65–77 (2016).
A. I. Prilepko, D. G. Orlovsky, and I. A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker, New York (2000).
A. Sh. Lyubanova and A. V. Velisevich, “Inverse problems for the stationary and pseudoparabolic equations of diffusion,” Appl. Anal. 98, No. 11, 1997–2010 (2019).
A. V. Velisevich, “On an inverse problem for the stationary equation with a boundary condition of the third type,” J. Sib. Fed. Univ., Math. Phys. 14, No. 5, 659–666 (2021).
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Translated from Problemy Matematicheskogo Analiza 122, 2023, pp. 79-85.
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Lyubanova, A.S., Velisevich, A.V. An Inverse Problem for a Quasilinear Elliptic Equation. J Math Sci 270, 591–599 (2023). https://doi.org/10.1007/s10958-023-06370-9
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DOI: https://doi.org/10.1007/s10958-023-06370-9