论文标题
氦产量扩散方程的逆随机源问题，由分数布朗运动驱动
An inverse random source problem for the Helium production-diffusion equation driven by a fractional Brownian motion
论文作者
论文摘要
在本文中，我们将氦浓度的预测视为由分数布朗运动扰动的空间可变源项的函数。对于直接问题，我们表明它已经有良好的态度，并且在某些条件下具有独特的温和解决方案。对于逆问题，给出了唯一性和不稳定性。同时，我们从最终数据U（R，T）的期望和协方差确定源的统计属性。最后，给出了数值工具以验证提出的重建的有效性。
In this paper, we consider the prediction of the helium concentrations as function of a spatially variable source term perturbed by fractional Brownian motion. For the direct problem, we show that it is well-posed and has a unique mild solution under some conditions. For the inverse problem, the uniqueness and the instability are given. In the meanwhile, we determine the statistical properties of the source from the expectation and covariance of the final-time data u(r,T). Finally, numerical implements are given to verify the effectiveness of the proposed reconstruction.
