A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations with convex Hamiltonians
A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations with convex Hamiltonians
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DOI：
10.1016/j.anihpc.2013.10.005
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发表时间：
2012-12
影响因子：
1.9
通讯作者：
F. Cagnetti;D. Gomes;Hiroyoshi Mitake;H. Tran
中科院分区：
文献类型：
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作者：
F. Cagnetti;D. Gomes;Hiroyoshi Mitake;H. Tran
研究了具有可能退化扩散项的粘性Hamilton-Jacobi方程的大时间渐近性。我们建立了新的结果的收敛性，这是第一个一般的方程，既不是一致抛物，也不是一阶。我们的方法是基于非线性伴随方法和推导新的估计长时间平均的影响。它也扩展到弱耦合系统的情况。
We investigate large-time asymptotics for viscous Hamilton–Jacobi equations with possibly degenerate diffusion terms. We establish new results on the convergence, which are the first general ones concerning equations which are neither uniformly parabolic nor first order. Our method is based on the nonlinear adjoint method and the derivation of new estimates on long time averaging effects. It also extends to the case of weakly coupled systems.