Asymptotic Solutions of Hamilton–Jacobi Equations with Semi-Periodic Hamiltonians
Asymptotic Solutions of Hamilton–Jacobi Equations with Semi-Periodic Hamiltonians
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DOI：
10.1080/03605300701257427
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发表时间：
2008-04
影响因子：
1.9
通讯作者：
Naoyuki Ichihara;H. Ishii
中科院分区：
文献类型：
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作者：
Naoyuki Ichihara;H. Ishii
研究了Hamilton Jacobi方程Cauchy问题粘性解的长时间行为。我们证明了，如果H（x，p）在p中是强制的，严格的弱凸的，并且在x中是上半周期的，那么柯西问题的任何解对于任何下半概周期的初始函数都“收敛”到一个渐近解.
We study the long time behavior of viscosity solutions of the Cauchy problem for Hamilton–Jacobi equations in ℝ n . We prove that if the Hamiltonian H(x, p) is coercive and strictly convex in a mild sense in p and upper semi-periodic in x, then any solution of the Cauchy problem “converges” to an asymptotic solution for any lower semi-almost periodic initial function.