Inverse problems for a quasilinear strongly damped wave equation arising in nonlinear acoustics

2023/09/21 by Li Li, Yang Zhang, Li, Li +1 · 1 citation
Computer Science · Mathematics · #35G30 #35L70 #35R30 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2309.11775

openalex publication_date 2023/09/21 · openalex created_date 2023/09/23 · openalex updated_date 2026/07/28

Abstract

We consider inverse problems for a Westervelt equation with a strong damping and a time-dependent potential q. We first prove that all boundary measurements, including the initial data, final data, and the lateral boundary measurements, uniquely determine q and the nonlinear coefficient β. The proof is based on complex geometric optics construction and the approach proposed by Isakov. Further, by considering fundamental solutions supported in a half-space constructed by Hörmander, we prove that with vanishing initial conditions the Dirichlet-to-Neumann map determines q and β.

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• Simultaneous determination of wave speed, diffusivity and nonlinearity in the Westervelt equation using complex time-periodic solutions

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