Abstract

For a singularly perturbed reaction–diffusion–advection equation, called in applications a Burgers-type equation and having a time-periodic solution with an internal transition layer, asymptotic analysis is used to solve some inverse problems of reconstructing model parameters (determining the linear amplification factor and boundary conditions) from known information about the observed solution of the direct problem in a given time interval (period). Numerical experiments demonstrating the efficiency of the approach proposed are conducted.

中文翻译：

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Burgers型方程系数反问题的渐近解

摘要

对于奇摄动的反应-扩散-对流方程，在应用中称为Burgers型方程，并且具有带有内部过渡层的时间周期解，使用渐近分析来解决重构模型参数的一些反问题（确定线性放大因子和边界条件）的已知信息，这些信息是在给定的时间间隔（周期）中观察到的直接问题的解决方案。进行了数值实验，证明了所提出方法的效率。