# An observability estimate for the wave equation and applications to the Neumann boundary controllability for semi-linear wave equations

arXiv: https://arxiv.org/abs/2409.07214 · HTML: https://mlsanity.com/paper/2409.07214/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Initial condition recovery in nonlinear damped viscous photoacoustic tomography using a convolutional neural network-guided gradient-free optimization framework](https://mlsanity.com/paper/2610.01015/) (2026)

## Abstract (arXiv)

We give a boundary observability result for a 1d wave equation with a potential. We then deduce with a Schauder fixed-point argument the existence of a Neumann boundary control for a semi-linear wave equation partialtty - partialxxy + f(y) = 0 under an optimal growth assumption at infinity on f of the type sln2s. Moreover, assuming additional assumption on f', we construct a minimizing sequence which converges to a control. Numerical experiments illustrate the results. This work extends to the Neumann boundary control case the work of Zuazua in 1993 and the work of M"unch and Tr'elat in 2022.