Work

Inverse problems for nonlinear progressive waves

Year: 2025

Type: article

Abstract: We propose and study several inverse problems associated with the nonlinear progressive waves that arise in infrasonic inversions. The nonlinear progressive equation is of a quasilinear form $$\partial _t^2 u=\Delta f(x, u)$$ ∂ t 2 u = Δ f ( x , u ) with $$f(x, u)=c_1(x) u+c_2(x) u^n$$ f ( x , u ) = c 1 ( x ) u + c 2 ( x ) u n , $$n\ge 2$$ n ≥ 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.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-02964-0

Authors: Yan Jiang, Hongyu Liu, Tianhao Ni, Kai Zhang

Institutions: Jilin University, City University of Hong Kong, Zhejiang University

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190