NONMONOTONICITY OF PRINCIPAL EIGENVALUES IN DIFFUSION RATE FOR SOME NON-SELF-ADJOINT OPERATORS WITH LARGE ADVECTION

Shuang Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The paper is concerned with the monotonicity of the principal eigenvalues with respect to diffusion rate for two classes of non-self-adjoint operators: time-periodic parabolic operators and elliptic operators with shear flow. These operators behave similarly to some averaged self-adjoint elliptic operators when the frequency or flow amplitude, referred to as advection rate, is sufficiently large. It was conjectured in [S. Liu and Y. Lou, J. Funct. Anal., 282 (2022), 109338] that the principal eigenvalues are monotone in diffusion rate for large advection, similarly to those self-adjoint elliptic operators. We provide some counterexamples to the conjecture by establishing the high order expansion of the principal eigenvalues for sufficiently large diffusion and advection rates.

Original languageEnglish
Pages (from-to)6025-6056
Number of pages32
JournalSIAM Journal on Mathematical Analysis
Volume56
Issue number5
DOIs
Publication statusPublished - 2024

Keywords

  • asymptotic behavior
  • elliptic operators with shear flow
  • monotonicity
  • principal eigenvalue
  • time-periodic parabolic operators

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Liu, S. (2024). NONMONOTONICITY OF PRINCIPAL EIGENVALUES IN DIFFUSION RATE FOR SOME NON-SELF-ADJOINT OPERATORS WITH LARGE ADVECTION. SIAM Journal on Mathematical Analysis, 56(5), 6025-6056. https://doi.org/10.1137/23M1603947