论文标题
关于Cahn-Hilliard方程中多个参数的独特性和稳定估计
On uniqueness and stable estimation of multiple parameters in the Cahn-Hilliard equation
论文作者
论文摘要
我们考虑了用于相分离的Cahn-Hilliard模型中多个参数的可识别性和稳定的数值估计。假定相位分数的空间解析测量值是可访问的，从而确定了单个和多个参数的可识别性，直到某些缩放量表不向导。为参数识别问题的稳定数值解决方案提出了一种正则化方程误差方法，并在合理的假设上对数据噪声进行了证明，正则化近似值的收敛性。在数值测试中证明了理论结果和所提出的方法的生存能力。
We consider the identifiability and stable numerical estimation of multiple parameters in a Cahn-Hilliard model for phase separation. Spatially resolved measurements of the phase fraction are assumed to be accessible, with which the identifiability of single and multiple parameters up to certain scaling invariances is established. A regularized equation error approach is proposed for the stable numerical solution of the parameter identification problems, and convergence of the regularized approximations is proven under reasonable assumptions on the data noise. The viability of the theoretical results and the proposed methods is demonstrated in numerical tests.
