Well-posedness of Hamilton–Jacobi equations with Caputo’s time fractional derivative
Well-posedness of Hamilton–Jacobi equations with Caputo’s time fractional derivative
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DOI：
10.1080/03605302.2017.1324880
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发表时间：
2016-12
影响因子：
1.9
通讯作者：
Y. Giga;Tokinaga Namba
中科院分区：
文献类型：
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作者：
Y. Giga;Tokinaga Namba
摘要考虑了一类具有小于一阶Caputo时间分数阶导数的Hamilton-Jacobi方程。引入粘性解的概念，证明了周期边界条件下初值问题解的唯一存在性。为此，建立了比较原理和Perron方法。研究了关于导数阶数和标准阶数的稳定性。还讨论了解的正则性。我们的结果特别适用于具有变系数分数阶导数的线性迁移方程。
ABSTRACT A Hamilton–Jacobi equation with Caputo’s time fractional derivative of order less than one is considered. The notion of a viscosity solution is introduced to prove unique existence of a solution to the initial value problem under periodic boundary conditions. For this purpose, comparison principle as well as Perron’s method is established. Stability with respect to the order of derivative as well as the standard one is studied. Regularity of a solution is also discussed. Our results in particular apply to a linear transport equation with time fractional derivatives with variable coefficients.