四阶正则化YK方程弱解的存在唯一性 |
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引用本文: | 金正猛,杨孝平.四阶正则化YK方程弱解的存在唯一性[J].数学物理学报(A辑),2009,29(5):1265-1273. |
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作者姓名: | 金正猛 杨孝平 |
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作者单位: | 南京理工大学应用数学系,南京,210094 |
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基金项目: | 教育部博士点专项基金,南京理工大学博士生创新基金 |
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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L2, 这在图像处理中显得更为自然.
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关 键 词: | 存在性 唯一性 四阶抛物型方程 |
收稿时间: | 2007-05-21 |
修稿时间: | 2008-08-16 |
Existence and Uniqueness of Weak Solutions for a Fourth Order Regularized YK Equation |
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Institution: | Department of Applied Mathematics, Nanjing University of Science &|Technology, Nanjing 210094 |
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Abstract: | 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. |
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Keywords: | Existencezz Uniquenesszz Fourth order parabolic equationszz |
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