Limiting behavior of principal eigenvalues and eigenfunctions for a class of elliptic operators with degenerate large advection

S. Cano-Casanova, J. López-Gómez and M. Molina-Meyer

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 84-107

Abstract: In this paper we study, both numerically and analytically, the asymptotic behavior of the principal eigenfunction of (1.1), normalized by (1.2), as s↑+∞. Based on the numerical computations of this paper, we can prove that, under condition (Hm) below, φs approximates 1 and φs′ approximates 0, uniformly in [−1,1], as s↑+∞. As a byproduct of this result, we can derive the asymptotic behavior of the principal eigenvalue in a one-dimensional situation not previously covered by Chen and Lou (2008) and Peng and Zhou (2018), as we are working under minimal regularity assumptions on m(x). A recent result of Bai et al. (2025) shows that the principal eigenvalue might oscillate as s↑+∞ if m(x) is highly oscillatory. Thus, the lack of regularity of m(x) might severely affect the behavior of (λs,φs) as s↑+∞.

Keywords: Principal eigenfunction; Principal eigenvalue; Degenerate advection; Limiting behavior; Singular perturbations (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475426001163
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:84-107

DOI: 10.1016/j.matcom.2026.03.025

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().