Long-time Behavior of Solutions of Hamilton–Jacobi Equations with Convex and Coercive Hamiltonians
Long-time Behavior of Solutions of Hamilton–Jacobi Equations with Convex and Coercive Hamiltonians
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DOI：
10.1007/s00205-008-0170-0
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发表时间：
2009-11
影响因子：
2.5
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
研究了具有凸哈密顿量和强制哈密顿量的Hamilton-Jacobi方程粘性解的长时间行为，给出了当时间渐近于无穷大时，解收敛于渐近解的三个一般判据。我们应用这些准则得到了更具体的收敛到渐近解的充分条件，并用实例进行了检验。我们采用动力学的方法，基于弱KAM理论的工具，如极值曲线、Aubry集和解的表示公式，来进行这些研究。
We investigate the long-time behavior of viscosity solutions of Hamilton–Jacobi equations inwith convex and coercive Hamiltonians and give three general criteria for the convergence of solutions to asymptotic solutions as time goes to infinity. We apply the criteria to obtain more specific sufficient conditions for the convergence to asymptotic solutions and then examine them with examples. We take a dynamical approach, based on tools from weak KAM theory such as extremal curves, Aubry sets and representation formulas for solutions, for these investigations.