摘要
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.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2009年第5期1265-1273,共9页
Acta Mathematica Scientia
基金
教育部博士点专项基金(20030288002)
南京理工大学博士生创新基金资助
关键词
存在性
唯一性
四阶抛物型方程
Existence
Uniqueness
Fourth order parabolic equations
