In the present paper we prove an homogenisation result for a locally perturbed transport stochastic equation. The model is similar to the stochastic Burgers' equation and it is inspired by the LWR model. Therefore, the interest in studying this equation comes from it's application for traffic flow modelling. In the first part of paper we study the inhomogeneous equation. More precisely we give an existence and uniqueness result for the solution. The technical difficulties of this part come from the presence of the function $ \varphi $ under assumptions coherent for the model, which is giving the inhomogeneity with respect to the space variable, not present in the classical results. The second part of the paper is the homogenisation result in space.

中文翻译：

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随机粘性输运方程的均质化

在本文中，我们证明了局部扰动的运输随机方程的均化结果。该模型与随机Burgers方程相似，并且受LWR模型的启发。因此，研究此方程的兴趣来自其在交通流建模中的应用。在论文的第一部分中，我们研究了非齐次方程。更准确地说，我们给出了该解的存在性和唯一性结果。这部分的技术难题来自在模型连贯的假设下函数$ \ varphi $的存在，这给出了空间变量的不均匀性，这在经典结果中不存在。本文的第二部分是空间的均质化结果。