论文标题
基于卡尔曼的收缩原理，以重建非线性双曲线方程的潜力
The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations
论文作者
论文摘要
我们开发了一种有效且收敛的数值方法，用于求解从外侧Cauchy数据确定非线性双曲线方程的潜力的反问题。在我们的数值方法中，我们构造了一系列线性库奇问题的序列，其相应的解决方案会收敛到一个可用于有效计算出感兴趣的反问题的近似解决方案的函数。通过结合收缩原理和Carleman估计来确定收敛分析。我们使用准可逆性方法来数值解决线性库奇问题。提出了数值示例，以说明该方法的效率。
We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In our numerical method we construct a sequence of linear Cauchy problems whose corresponding solutions converge to a function that can be used to efficiently compute an approximate solution to the inverse problem of interest. The convergence analysis is established by combining the contraction principle and Carleman estimates. We numerically solve the linear Cauchy problems using a quasi-reversibility method. Numerical examples are presented to illustrate the efficiency of the method.
