We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. The system serves as a simplified model of the second harmonic generation process in a heterogeneous medium. We derive results on the uniqueness and stability of the inverse problem in the case of small boundary data based on the technique of first- and higher-order linearization. Numerical simulations are provided to illustrate the quality of reconstructions that can be expected from noisy data.

中文翻译：

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从内部数据恢复半线性亥姆霍兹方程组中的系数

我们研究半线性亥姆霍兹方程耦合系统的反问题，我们感兴趣的是根据热声成像等应用中测量的内部数据重建系统中的多个系数。该系统作为异质介质中二次谐波产生过程的简化模型。基于一阶和高阶线性化技术，我们得出了小边界数据情况下反问题的唯一性和稳定性的结果。提供数值模拟来说明可以从噪声数据中预期的重建质量。