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Singular free boundary problem from image processing
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DOI：10.1142/S0218202505000509.png)
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Abstract
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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.
Keywords:
nonlinear diffusion
image enhancement
singular solutions
free boundaries
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