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arXiv · 1803.10541

Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation

Jussi Korpela·Matti Lassas·Lauri Oksanen
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Abstract

An inverse boundary value problem for the 1+1 dimensional wave equation $(\partial_t^2 - c(x)^2 \partial_x^2)u(x,t)=0,\quad x\in\mathbb{R}_+$ is considered. We give a discrete regularization strategy to recover wave speed $c(x)$ when we are given the boundary value of the wave, $u(0,t)$, that is produced by a single pulse-like source. The regularization strategy gives an approximative wave speed $\widetilde c$, satisfying a H\"older type estimate $\| \widetilde c-c\|\leq C \epsilon^{\gamma}$, where $\epsilon$ is the noise level.

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Jussi Korpela, Matti Lassas, Lauri Oksanen. 2018-03-28. Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation. https://arxiv.org/abs/1803.10541

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