In the present paper, we devote our effort to Cauchy boundary value problems for biharmonic equations. In general, the investigated problem is ill-posed. Therefore, we develop a filter method to defeat the ill-posedness of the problem. Explicit convergence rate is established under both a priori and a posteriori parameter choice rules. Finally, a numerical example is presented to illustrate the ill-posedness of the problem as well as the effectiveness of the proposed method.

中文翻译：

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双调和方程柯西问题正则化的具有先验和后验参数选择的滤波方法

在本文中，我们致力于双调和方程的柯西边值问题。通常，所研究的问题是不适当的。因此，我们开发了一种过滤方法来克服问题的不适定性。在先验和后验参数选择规则下都建立了显式收敛速度。最后，给出了一个数值例子来说明问题的不适定性以及所提出方法的有效性。