In this paper, we study an inverse source problem for a degenerate and singular parabolic system where the boundary conditions are of Neumann type. We consider a problem with degenerate diffusion coefficients and singular lower-order terms, both vanishing at an interior point of the space domain. In particular, we address the question of well-posedness of the problem, and then we prove a stability estimate of Lipschitz type in determining the source term by data of only one component. Our method is based on Carleman estimates, cut-off procedures and a reflection technique.

中文翻译：

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具有Neumann边界条件的退化/奇异抛物方程组的反问题

在本文中，我们研究了边界条件为Neumann型的退化的奇异抛物系统的逆源问题。我们考虑一个退化的扩散系数和奇异的低阶项的问题，它们都在空间域的内部点消失。特别是，我们解决了问题的适定性问题，然后我们证明了Lipschitz类型的稳定性估计，它仅通过一个分量的数据确定源项。我们的方法基于Carleman估计，截止程序和反射技术。