What does this research mean for the field?

The asymptotic behavior of the generalized principal eigenvalue for Hamilton-Jacobi-Bellman equations under large perturbations can be reduced to a one-dimensional optimization problem, accommodating non-polynomial growth, general diffusion operators, and asymptotically radial coefficients. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To characterize the ergodic problem and determine the asymptotic behavior of generalized principal eigenvalues for Hamilton–Jacobi–Bellman equations under large potential perturbations.

August 27, 2026Nonlinear Differential Equations and Applications NoDEAOpen Access

Asymptotic behavior of the generalized principal eigenvalue for Hamilton–Jacobi–Bellman equations with asymptotically radial data

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Authors

ECEmmanuel ChasseigneUniversité de Tours NINaoyuki IchiharaAoyama Gakuin University

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Implication

Mathematical analysis demonstrates eigenvalue asymptotics for Hamilton–Jacobi–Bellman equations with inward drifts, indicating that multidimensional problems simplify to one-dimensional optimization.

Key Points

To characterize the ergodic problem and determine the asymptotic behavior of generalized principal eigenvalues for Hamilton–Jacobi–Bellman equations under large potential perturbations.
Analyzed Hamilton–Jacobi–Bellman equations featuring convex, superlinear Hamiltonians, generalized diffusion operators, and inward-pointing drift vectors.
Extended analytical techniques to accommodate non-polynomial growth conditions and asymptotically radially symmetric data.
Constructed an asymptotic estimation framework linking the eigenvalue problem to stochastic control interpretations.
Successfully established the asymptotic behavior of the generalized principal eigenvalue under large perturbations of the potential function.
Reduced the multidimensional asymptotic evaluation directly to a simple, solvable one-dimensional optimization problem defined by the initial data.

Cite This Study

Chasseigne et al. (2026) studied this question.

synapsesocial.com/papers/6a8fe9c910c91c1e92621c30 https://doi.org/10.1007/s00030-026-01262-8

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Asymptotic behavior of the generalized principal eigenvalue for Hamilton–Jacobi–Bellman equations with asymptotically radial data

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Implication

Key Points

Cite This Study

Asymptotic behavior of the generalized principal eigenvalue for Hamilton–Jacobi–Bellman equations with asymptotically radial data

Discussion

Member takes

Implication

Key Points

Cite This Study

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