Introduction to inverse problems for non-linear partial differential equations
Analysis of PDEs
2025-03-18 v1
Abstract
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is based on self-interaction of linearized waves or other solutions in the presence of non-linearities. Multiple linearization has successfully been used to solve inverse problems for non-linear equation which are still unsolved for the corresponding linear equations.
Cite
@article{arxiv.2503.12448,
title = {Introduction to inverse problems for non-linear partial differential equations},
author = {Matti Lassas},
journal= {arXiv preprint arXiv:2503.12448},
year = {2025}
}
Comments
The paper will appear in the proceedings of the 9th European Congress of Mathematics (9ECM) held in Sevilla, 2024