Stable inversion of potential in nonlinear wave equations with cubic nonlinearity
Analysis of PDEs
2025-01-22 v2
Abstract
This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower order coefficients. The new ingredients of our approach include trilinear approximations of nonlinear response operators, symbol estimates of distorted plane waves, and lower order symbol calculus.
Cite
@article{arxiv.2501.00748,
title = {Stable inversion of potential in nonlinear wave equations with cubic nonlinearity},
author = {Xi Chen and Shuai Lu and Ruochong Zhang},
journal= {arXiv preprint arXiv:2501.00748},
year = {2025}
}
Comments
The exponents of the error bounds in (1.4)-(1.5) are slightly improved