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This article is cited in 6 scientific papers (total in 6 papers)
Inverse problem for wave equation with polynomial nonlinearity
V. G. Romanova, T.V. Buguevaba a Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
Abstract:
For a wave equation containing nonlinearity in the form of a $n$-th order polynomial, the problem of determining the coefficients of the polynomial depending on the variable $x\in \mathbb{R}^3$ is studied. Plane waves propagating with a sharp front in a homogeneous medium in the direction of a unit vector $\boldsymbol\nu$ and falling on inhomogeneity localized inside some ball $B(R)$ are considered. It is assumed that the solutions of forward problems for all possible $\nu$ can be measured at points of the
boundary of this ball at time close to the arrival of the wave front. It is shown that the solution of the inverse problem is reduced to a series of X-ray tomography problems.
Keywords:
semilinear wave equation, inverse problem, plane waves, X-ray tomography, uniqueness.
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Received: 31.10.2022 Revised: 02.11.2022 Accepted: 12.01.2023
Citation:
V. G. Romanov, T.V. Bugueva, “Inverse problem for wave equation with polynomial nonlinearity”, Sib. Zh. Ind. Mat., 26:1 (2023), 142–149; J. Appl. Industr. Math., 17:1 (2023), 163–167
Linking options:
https://www.mathnet.ru/eng/sjim1220 https://www.mathnet.ru/eng/sjim/v26/i1/p142
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