非线性三阶声学方程系数的稳定确定
Stable determination of coefficients for the nonlinear third-order acoustic equations
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中文总结 AI 辅助
本文针对广义Jordan-Moore-Gibson-Thompson方程，利用Dirichlet-to-Neumann映射和有限差分线性化及几何光学方法，同时稳定确定摩擦、阻尼、势和非线性系数，并获Hölder型稳定性估计。
中文摘要 AI 辅助
本文研究了一类具有Westervelt型非线性和空间依赖系数的广义Jordan-Moore-Gibson-Thompson方程的逆边值问题。该三阶（时间上）双曲方程模拟了粘性和热弛豫介质中的非线性超声传播。假设扩散率和声速先验已知，我们研究了从相应的Dirichlet-to-Neumann映射同时稳定确定摩擦系数、弱阻尼系数、势函数和非线性系数的问题。证明结合了有限差分线性化方法与高斯束和几何光学解的构造。这些论证在叶状条件下将逆问题简化为（衰减的）测地线射线变换的稳定性估计。因此，我们获得了恢复线性和非线性系数的Hölder型稳定性估计。
英文摘要
In this paper, we study an inverse boundary value problem for a generalized Jordan-Moore-Gibson-Thompson equation with Westervelt-type nonlinearity and space-dependent coefficients. This third-order (in time) hyperbolic equation models nonlinear ultrasound propagation in viscous and thermally relaxing media. Assuming that the diffusivity and the sound speed are known a priori, we investigate the simultaneous stable determination of the friction coefficient, the weak damping coefficient, the potential, and the nonlinear coefficient from the associated Dirichlet-to-Neumann map. The proof combines the finite-difference linearization method with the construction of Gaussian beam and geometric optics solutions. These arguments reduce the inverse problem to stability estimates for (attenuated) geodesic ray transforms under the foliation condition. As a consequence, we obtain Hölder-type stability estimates of recovering the linear and nonlinear coefficients.
发表机构
- School of Mathematics and Statistics, Northwestern Polytechnical University（西北工业大学数学与统计学院）
- School of Mathematics, Zhejiang University（浙江大学数学系）
- School of Mathematical Sciences and LPMC, Nankai University（南开大学数学科学学院）
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