This paper is devoted to some inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. It is shown in several generic scenarios that one can uniquely determine the nonlinearity and/or the sources by using passive or active boundary observations. In order to exploit the nonlinearity and the sources simultaneously, we develop a new technique, which combines the observability for linear wave equations and an approximation property with higher order linearization for the semilinear hyperbolic equation.

中文翻译：

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确定具有未知源和非线性的非线性双曲系统

本文致力于研究与瞬态半线性双曲方程相关的一些逆边界问题，其中非线性和源（包括初始位移和初始速度）都是未知的。在几种通用场景中表明，人们可以通过使用被动或主动边界观测来唯一地确定非线性和/或源。为了同时利用非线性和源，我们开发了一种新技术，它将线性波动方程的可观测性和半线性双曲方程的高阶线性化近似特性结合起来。