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arXiv · 2308.07808

Inverse problems for nonlinear progressive waves

Yan Jiang·Hongyu Liu·Tianhao Ni·Kai Zhang
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Abstract

We propose and study several inverse problems associated with the nonlinear progressive waves that arise in infrasonic inversions. The nonlinear progressive equation (NPE) is of a quasilinear form $\partial_t^2 u=\Delta f(x, u)$ with $f(x, u)=c_1(x) u+c_2(x) u^n$, $n\geq 2$, and can be derived from the hyperbolic system of conservation laws associated with the Euler equations. We establish unique identifiability results in determining $f(x, u)$ as well as the associated initial data by the boundary measurement. Our analysis relies on high-order linearisation and construction of proper Gaussian beam solutions for the underlying wave equations. In addition to its theoretical interest, we connect our study to applications of practical importance in infrasound waveform inversion.

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Yan Jiang, Hongyu Liu, Tianhao Ni, Kai Zhang. 2023-08-15. Inverse problems for nonlinear progressive waves. https://arxiv.org/abs/2308.07808

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