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Vanishing curvature viscosity for front propagation

机译：消失的曲率粘度，用于正面传播

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In this paper we study the front propagation with constant speed and small curvature viscosity. We first investigate two related problems of conservation laws, one of which is on the nonlinear viscosity methods for the conservation laws, and the other one is on the structure of solutions to conservation laws with L-1 initial data. We show that the nonlinear viscosity methods approaching the piecewise smooth solutions with finitely many discontinuity for convex conservation laws have the first-order rate of L-1-convergence. The solutions of conservation laws with L-1 initial data are shown to be bounded after t > 0 if all singular points of initial data are from shocks. These results suggest that the front propagation with constant speed and a small curvature viscosity will approach the front movements with a constant speed, as the small parameter goes to zero. After the front breaks down, the cusps will disappear promptly and corners will be formed. (C) 2000 Academic Press. [References: 20]
机译：在本文中，我们研究了具有恒定速度和小曲率粘度的前沿传播。首先，我们研究了守恒律的两个相关问题，一个是关于守恒律的非线性粘度方法，另一个是关于具有L-1初始数据的守恒律解的结构。我们表明，对于凸守恒定律，具有有限多个不连续点的分段光滑解的非线性粘度方法具有L-1收敛的一阶速率。如果初始数据的所有奇异点都来自冲击，则具有L-1初始数据的守恒定律的解表明在t> 0之后是有界的。这些结果表明，当小参数变为零时，具有恒定速度和较小曲率粘度的前部传播将以恒定速度接近前部运动。前端破裂后，尖点将立即消失并形成角。 （C）2000学术出版社。 [参考：20]

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