Dept. Math, Hokkaido Univ. EPrints Server

Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation

Preprint Series # 778
Giga, Yoshikazu and Kuroda, Hirotoshi and Yamazaki, Noriaki Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation. (2006);

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Abstract

We consider a gradient flow system of total variation with constraint. Our system is often used in the color image processing to remove a noise from picture. In particular, we want to preserve the sharp edges of picture and color chromaticity. Therefore, the values of solutions to our model is constrained in some fixed compact Riemannian manifold. By this reason, it is very difficult to analyze such a problem, mathematically. The main object of this paper is to show the global solvability of a constrained singular diffusion equation associated with total variation. In fact, by using abstract convergence theory of convex functions, we shall prove the existence of solutions to our models with piecewise constant initial and boundary data.

Item Type:Preprint
Subjects:68-xx COMPUTER SCIENCE
35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1521