Well-posedness and inverse problems for semilinear nonlocal wave equations

Yi Hsuan Lin, Teemu Tyni, Philipp Zimmermann*

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摘要

This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main challenge is due to the low regularity of the solutions of linear nonlocal wave equations. We then turn to an inverse problem of recovering the nonlinearity of the equation. More precisely, we show that the exterior Dirichlet-to-Neumann map uniquely determines homogeneous nonlinearities of the form f(x,u) under certain growth conditions. On the other hand, we also prove that initial data can be determined by using passive measurements under certain nonlinearity conditions. The main tools used for the inverse problem are the unique continuation principle of the fractional Laplacian and a Runge approximation property. The results hold for any spatial dimension n∈N.

原文English
文章編號113601
期刊Nonlinear Analysis, Theory, Methods and Applications
247
DOIs
出版狀態Published - 10月 2024

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