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Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton-Jacobi equations

Abstract : This paper is concerned with the ergodic problem for superquadratic viscous Hamilton-Jacobi equations with exponent m > 2. We prove that the generalized principal eigenvalue of the equation converges to a constant as m → ∞, 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 m = 2, 2 < m < ∞, and the limiting case m = ∞.
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Submitted on : Sunday, March 20, 2016 - 12:11:33 PM
Last modification on : Sunday, March 29, 2020 - 6:22:12 PM
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  • HAL Id : hal-01291015, version 1
  • ARXIV : 1603.07461

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Emmanuel Chasseigne, Naoyuki Ichihara. Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton-Jacobi equations. Nonlinear Differential Equations and Applications, Springer Verlag, 2016, 23, pp.1-17. ⟨hal-01291015⟩

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