四阶正则化YK方程弱解的存在唯一性

Existence and Uniqueness of Weak Solutions for a Fourth Order Regularized YK Equation

该文针对图像处理中YK方程理论上的不适定性,提出了正则化的YK方程,证明了正则化的YK方程在有界区域上弱解的存在唯一性.而且,该文只要求初始数据属于L^2,这在图像处理中显得更为自然.

In this paper the authors propose the regularized YK equation based on the ill posed properties for the YK equation in image processing.They prove the existence and uniqueness of weak solution of the regularized equation in bounded domains.Furthermore,it is only assumed that the initial data belong to L2,which is more natural in image processing.