# On breakdown of solutions of a constrained gradient system of total variation

Preprint Series # 639
Giga, Yoshikazu and Kuroda, Hirotoshi On breakdown of solutions of a constrained gradient system of total variation. (2004);

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## Abstract

A gradient system of total variation is considered for a mapping from the unit disk to the unit sphere in ${\bf R}^3$. For a class of initial data it is shown that a solution of its Dirichlet problem loses its smoothness in finite time.

Item Type: Preprint 35-xx PARTIAL DIFFERENTIAL EQUATIONS 144