Singular free boundary problem from image processing

被引：15
作者：
Amadori, AL
Vázquez, JL
机构：
[1] CNR, IAC, I-00161 Rome, Italy
[2] Univ Salerno, DIIMA, I-84084 Fisciano, Sa, Italy
[3] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2005年 / 15卷 / 05期
关键词：
nonlinear diffusion; image enhancement; singular solutions; free boundaries;
D O I：
10.1142/S0218202505000509
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a degenerate nonlinear parabolic equation with moving boundaries which arises in the study of the technique of contour enhancement in image processing. In order to obtain mass concentration at the contour, singular data are imposed at the free boundary, leading to a nonstandard free boundary problem. Our main results are: (i) the well-posedness for the singular problem, without monotonicity assumptions on the initial datum, and (ii) the convergence of the approximation by means of combustion-type free-boundary problems.
引用
收藏
页码：689 / 715
页数：27
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