The inverse source problems for nonlinear advection-diffusion-reaction models with image-type measurement data are considered. The use of the sensitivity operators, constructed of the ensemble of adjoint problem solutions, allows transforming the inverse problems stated as the systems of nonlinear PDE to a family of operator equations depending on the given set of functions in the space of measurement results. The tangential cone conditions for the resulting operator equations are studied. Newton-Kantorovich type methods are applied for the solution of the operator equations. The algorithms are numerically evaluated on an inverse source problem of atmospheric chemistry.

中文翻译：

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具有图像类型测量的对流扩散反应模型逆源问题中伴随集成方法的收敛性分析

考虑具有图像类型测量数据的非线性对流扩散反应模型的逆源问题。由伴随问题解的集合构成的灵敏度算子的使用，允许根据测量结果空间中给定的一组函数将表示为非线性PDE系统的反问题转换为一系列算子方程。研究了所得算子方程的切锥条件。牛顿-坎托罗维奇类型方法用于算子方程的解。在大气化学反源问题上对算法进行了数值评估。