Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton-Jacobi equations
Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton-Jacobi equations
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超二次粘性 Hamilton-Jacobi 方程广义主特征值的定性性质
DOI：
10.1007/s00030-016-0422-x
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
E. Chasseigne and N. Ichihara
中科院分区：
文献类型：
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作者：
Yasuo Komori-Furuya;E. Chasseigne and N. Ichihara
研究了具有指数的超二次粘性Hamilton-Jacobi方程的遍历问题。我们证明了方程的广义主特征值收敛于常数，并且极限与带梯度约束的遍历问题的广义主特征值一致。我们还研究了势函数扰动下广义主特征值的一些定性性质。事实证明，根据、和极限情况，会发生不同的情况。
This paper is concerned with the ergodic problem for superquadratic viscous Hamilton–Jacobi equations with exponent. We prove that the generalized principal eigenvalue of the equation converges to a constant as, and that the limit coincides with the generalized principal eigenvalue of an ergodic problem with gradient constraint. We also investigate some qualitative properties of the generalized principal eigenvalue with respect to a perturbation of the potential function. It turns out that different situations take place according to,, and the limiting case.