In this paper, we consider the problem of finding the source distribution for the linear inhomogeneous biparabolic equation when the measured output data is given in the form of the final overdetermination. The problem is severely ill-posed in the sense of Hadamard. First, we apply a general filter method to regularize the linear nonhomogeneous problem. Then, we give a regularized solution and consider the convergence between the regularized solution and the sought solution. Under an a priori assumption on the exact solution, we obtain some convergence estimates between the regularized solution and the sought solution.

中文翻译：

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用最终数据识别双抛物线方程的右侧

在本文中，我们考虑在以最终超定形式给出测量输出数据时寻找线性非齐次双抛物方程的源分布的问题。这个问题在 Hadamard 的意义上是严重不适定的。首先，我们应用一种通用过滤方法来正则化线性非齐次问题。然后，我们给出一个正则化解，并考虑正则化解和寻求的解之间的收敛性。在对精确解的先验假设下，我们获得了正则化解和寻求解之间的一些收敛估计。