A nonlinear parabolic equation with discontinuity in the highest order and applications
A nonlinear parabolic equation with discontinuity in the highest order and applications
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最高阶不连续的非线性抛物线方程及其应用
DOI：
10.1016/j.jde.2015.09.022
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发表时间：
2016
影响因子：
2.4
通讯作者：
Qing Liu
中科院分区：
文献类型：
--
作者：
Robin Ming Chen;Qing Liu
本文建立了一类在未知函数的二阶导数上具有符号函数型不连续性的非线性抛物方程的粘性解理论。我们修正了经典粘性解的定义，证明了解的存在唯一性。这些结果与曲线运动的极限行为有关，其曲率的幂非常小，这在图像处理中有应用。我们还讨论了该方程与一维全变差流的关系。
In this paper we establish a viscosity solution theory for a class of nonlinear parabolic equations with discontinuities of the sign function type in the second derivatives of the unknown function. We modify the definition of classical viscosity solutions and show uniqueness and existence of the solutions. These results are related to the limit behavior for the motion of a curve by a very small power of its curvature, which has applications in image processing. We also discuss the relation between our equation and the total variation flow in one space dimension.