论文标题
具有非线性吸收的散射介质中波传播的传输模型
Transport models for wave propagation in scattering media with nonlinear absorption
论文作者
论文摘要
这项工作认为在高散射的媒介中，高频率波的传播发生在非线性性质的物理吸收中。使用Wigner变换和多尺度分析的经典工具，我们得出了半线性辐射传输模型的相位强度和此类传输模型的扩散极限。作为一种应用，我们考虑了半线性传输方程的一个反问题，在该方程中，我们从其溶液的功能中重建方程的吸收系数。我们在反问题上获得了唯一性结果。
This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear radiative transport models for the phase-space intensity and the diffusive limits of such transport models. As an application, we consider an inverse problem for the semilinear transport equation, where we reconstruct the absorption coefficients of the equation from a functional of its solution. We obtain a uniqueness result on the inverse problem.
