Homogenization of the Cauchy Problem for Hamilton-Jacobi Equations
Homogenization of the Cauchy Problem for Hamilton-Jacobi Equations
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Hamilton-Jacobi 方程柯西问题的齐次化
DOI：
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发表时间：
1999
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通讯作者：
H. Ishii
中科院分区：
文献类型：
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作者：
H. Ishii
研究了周期系数Hamilton-Jacobi方程Cauchy问题解在周期频率趋于无穷大时的渐近性态。极限函数被表征为Hamilton-Jacobi方程的唯一解，其哈密顿量由相应的胞腔问题确定。我们的结果适用于初始数据周期性振荡的情况，所以在空间和时间变量的哈密顿量。
We study the asymptotic behavior of solutions of the Cauchy problem for Hamilton-Jacobi equations with periodic coefficients as the frequency of periodicity tends to infinity. The limit functions are characterized as unique solutions of Hamilton-Jacobi equations with the Hamiltonians determined by the corresponding cell problems. Our result applies to the case where the initial data oscillate periodically and so does the Hamiltonian both in the spatial and time variables.