Short time uniqueness results for solutions of nonlocal and non-monotone geometric equations
Short time uniqueness results for solutions of nonlocal and non-monotone geometric equations
复制标题
非局部和非单调几何方程解的短时唯一性结果
DOI：
10.1007/s00208-011-0648-1
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发表时间：
2012
影响因子：
1.4
通讯作者：
三竹大寿
中科院分区：
文献类型：
--
作者：
Guy Barles;Olivier Ley;三竹大寿
我们描述了一种方法，以显示短时间的唯一性结果的粘性解的一般非局部和非单调的二阶几何方程中产生的前传播问题。我们的方法基于解的一些梯度下界。这些估计是至关重要的，以获得正则性的前，允许处理非局部项的方程。给出了位错型方程、FitzHugh-Nagumo型系统的渐近方程和依赖于前沿Lebesgue测度的方程的初值问题的短时唯一性结果。
We describe a method to show short time uniqueness results for viscosity solutions of general nonlocal and non-monotone second-order geometric equations arising in front propagation problems. Our method is based on some lower gradient bounds for the solution. These estimates are crucial to obtain regularity properties of the front, which allow to deal with nonlocal terms in the equations. Applications to short time uniqueness results for the initial value problems for dislocation type equations, asymptotic equations of a FitzHugh–Nagumo type system and equations depending on the Lebesgue measure of the fronts are presented.