May 14, 2024Open Access

Principal eigenvalue for some elliptic operators with large drift: Neumann boundary conditions

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Authors

SLShuang LiuBeijing Institute of Technology YLYuan LouShanghai Jiao Tong University MZMaolin ZhouNankai University

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Implication

Theoretical analysis reveals principal eigenvalue asymptotics for elliptic operators with large drift, highlighting their dependence on connected components within omega-limit sets.

Key Points

Asymptotic behavior of the principal eigenvalue for two-dimensional elliptic operators with infinite drift rate is completely determined by connected components of the omega-limit set.
Analysis of ordinary differential equations associated with the drift term resolves limits across stable fixed points, stable limit cycles, and homoclinic orbits without degeneracy.
Highlights how singular limits in diffusion processes connect to dynamical systems, providing a framework for analyzing degenerate regimes and drift-driven concentration phenomena.

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Liu et al. (2024) studied this question.

synapsesocial.com/papers/68e6a4e2b6db643587627d94 https://doi.org/10.48550/arxiv.2405.09031

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Implication

Theoretical analysis reveals principal eigenvalue asymptotics for elliptic operators with large drift, highlighting their dependence on connected components within omega-limit sets.

Principal eigenvalue for some elliptic operators with large drift: Neumann boundary conditions

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Implication

Key Points

Cite This Study

Principal eigenvalue for some elliptic operators with large drift: Neumann boundary conditions

Discussion

Member takes

Implication

Key Points

Cite This Study

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