An approach to solving coefficient inverse problems for nonlinear reaction-diffusion-advection equations is proposed. As an example, we consider an inverse problem of restoring a coefficient in a nonlinear Burgers-type equation. One of the features of the inverse problem is a use of additional information about the position of a reaction front. Another feature of the approach is a use of asymptotic analysis methods to select a good initial guess in a gradient method for minimizing a cost functional that occurs when solving the coefficient inverse problem. Numerical experiments demonstrate the effectiveness of the proposed approach.

中文翻译：

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具有反应前沿位置数据的非线性反应扩散对流型奇摄动方程的系数反问题

提出了一种求解非线性反应扩散对流方程系数反问题的方法。例如，我们考虑一个还原非线性Burgers型方程中系数的反问题。反问题的特征之一是使用有关反应前沿位置的附加信息。该方法的另一个特征是使用渐近分析方法来选择梯度方法中的良好初始猜测，以最小化求解系数反问题时出现的成本函数。数值实验证明了该方法的有效性。