In this paper we study an identification problem related to a nonlinear parabolic system. This system, called the nonlinear single phase mud filtrate invasion model, arises in the study of the mud filtrate invasion phenomenon and is presented in Boaca and Boaca (2018). Our objective is to determine the minimal value of the oil reservoir permeability starting from the observed values of the mud filtrate concentration at some time $T$. We reduce this identification problem to a nonlinear optimal control problem. We prove the existence of an optimal control and obtain the optimal condition. The influence of the noisy measurements and some numerical results are also presented.

在本文中，我们研究与非线性抛物线系统有关的识别问题。该系统称为非线性单相泥浆滤液入侵模型，是在研究泥浆滤液入侵现象时出现的，并在Boaca和Boaca（2018）中提出。我们的目标是根据一段时间内泥浆滤液浓度的观测值确定油藏渗透率的最小值$Ť$。我们将此识别问题简化为非线性最优控制问题。我们证明了最优控制的存在并获得了最优条件。还介绍了噪声测量的影响和一些数值结果。