发表机构
Indian Institute of Technology Ropar（印度技术学院罗帕尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对半线性波动方程，通过二阶线性化与几何光学方法，首次建立了从Dirichlet-to-Neumann映射同时稳定恢复阻尼、线性势和非线性势系数的Hölder型估计。
AI 中文摘要
我们考虑一个逆问题，涉及在 $\mathbb{R}^n$（$n\geq 2$）的有界域中，具有与时间无关的阻尼、线性势和非线性势系数的半线性波动方程。主要目标是建立从相关的Dirichlet-to-Neumann映射同时恢复这些系数的稳定性估计。我们的方法将二阶线性化与适当构造的几何光学和渐近解相结合。在适当的先验界条件下，我们建立了恢复半线性波动方程中出现的三个系数中每一个的Hölder型稳定性估计。据我们所知，这是在半线性波动方程中同时确定与时间无关的阻尼、线性和非线性势的首个稳定性结果。
英文摘要
We consider an inverse problem for a semilinear wave equation with time-independent damping, linear potential, and nonlinear potential coefficients in a bounded domain of $\mathbb{R}^n$ for $n\geq 2$. The main objective is to establish stability estimates for the simultaneous recovery of these coefficients from the associated Dirichlet-to-Neumann map. Our approach combines second-order linearization with suitably constructed geometric optics and asymptotic solutions. We establish Hölder-type stability estimates for the recovery of each of the three coefficients appearing in the semilinear wave equation under suitable a priori bounds on these coefficients. To the best of our knowledge, this is the first stability result for simultaneous determination of time-independent damping, linear and nonlinear potentials in a semiliner wave equation.
