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<p>In this paper, we study the stability in partial data inverse problems of determining the time-dependent viscosity and potential terms appearing in the Moore–Gibson–Thompson (MGT) equation in dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\ge 2\)</EquationSource> </InlineEquation>. The MGT equation, which is third order in time and of hyperbolic type, arises as a linearization of a model for nonlinear ultrasound wave propagation in viscous thermally relaxing fluids. By directly establishing some key Carleman estimates for the MGT equation and its dual, some suitable geometric optics solutions of exponential type are constructed. Then, the stability results in recovering the coefficients from partial observations on the boundary are obtained by means of the suitable geometric optics solutions together with the light ray and Fourier transforms.</p>

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Partial Data Inverse Problems of Determining Two Time-Dependent Coefficients for Third-Order Acoustic Equations

  • 期刊论文

  • 发表日期：

    2025年11月28日

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  • Song-Ren Fu,
  • Peng-Fei Yao,
  • Yongyi Yu

摘要

In this paper, we study the stability in partial data inverse problems of determining the time-dependent viscosity and potential terms appearing in the Moore–Gibson–Thompson (MGT) equation in dimension \(n\ge 2\) . The MGT equation, which is third order in time and of hyperbolic type, arises as a linearization of a model for nonlinear ultrasound wave propagation in viscous thermally relaxing fluids. By directly establishing some key Carleman estimates for the MGT equation and its dual, some suitable geometric optics solutions of exponential type are constructed. Then, the stability results in recovering the coefficients from partial observations on the boundary are obtained by means of the suitable geometric optics solutions together with the light ray and Fourier transforms.