一维Boussinesq方程反问题的不适定性实例构建

The Ill-Posed Example Construction of Inverse Problems of One-Dimensional Boussinesq Equation

摘要: 反问题的不适定性既包含问题本身的不适定性，也包含数值算法的不适定性。本文考虑一维Boussinesq方程反问题其问题本身的不适定性，即解的唯一性问题，着重指出反问题求解时附加条件的正确处理方式，同时构建了四个较为简单的实例，这些实例除了用于说明反问题的不适定性以外，还可以借助这四个实例进行进一步的数值仿真计算。

Abstract: The ill-posed nature of the inverse problem includes both the ill-posed nature of the problem itself and the ill-posed nature of the numerical algorithm. In this paper, we consider the ill-posedness of the inverse problem of one-dimensional Boussinesq equation, namely, the uniqueness of the solution. This paper points out the correct way to deal with the additional conditions when solving the inverse problem, and constructs four relatively simple examples, which are used not only to illustrate the unfitness of the inverse problem, but also to carry out subsequent numerical simulation calculation with the help of these four examples.