https://hdl.handle.net/1959.11/31760
Title: | Asymptotic behavior of the principal eigenvalue of a linear second order elliptic operator with small/large diffusion coefficient |
---|---|
Contributor(s): | Peng, Rui (author); Zhang, Guanghui (author); Zhou, Maolin (author) |
Publication Date: | 2019 |
Early Online Version: | 2019-11-21 |
DOI: | 10.1137/18M1217577 |
Handle Link: | https://hdl.handle.net/1959.11/31760 |
Abstract: | In this article, we are concerned with the following eigenvalue problem of a second order linear elliptic operator: -D∆∅ - 2α∇m(x) · ∇∅ + V(x)∅ = λ ∅ in Ω , complemented by a general boundary condition, including Dirichlet boundary condition and Robin boundary condition, ∂∅ ⁄ ∂n + β (x)∅ = 0 on ∂ Ω , where β ∈ C(∂ Ω) is allowed to be positive, sign-changing, or negative, and n(x) is the unit exterior normal to ∂ Ω at x. The domain Ω ⊂ ℝN is bounded and smooth, the constants D > 0 and α > 0 are, respectively, the diffusive and advection coefficients, and m ∈ C2(Ω), V ∈ C(Ω) are given functions. We aim to investigate the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as the diffusive coefficient D → 0 or D → ∞ . Our results, together with those of [X. F. Chen and Y. Lou, Indiana Univ. Math. J., 61 (2012), pp. 45-80; A. Devinatz, R. Ellis, and A. Friedman, Indiana Univ. Math. J., 23 (1973/74), pp. 991-1011; and A. Friedman, Indiana U. Math. J., 22 (1973), pp. 1005-1015] where the Neumann boundary case (i.e., β = 0 on ∂ Ω ) and Dirichlet boundary case were studied, reveal the important effect of advection and boundary conditions on the asymptotic behavior of the principal eigenvalue. |
Publication Type: | Journal Article |
Grant Details: | ARC/DE170101410 |
Source of Publication: | SIAM Journal on Mathematical Analysis, 51(6), p. 4724-4753 |
Publisher: | Society for Industrial and Applied Mathematics |
Place of Publication: | United States of America |
ISSN: | 1095-7154 0036-1410 |
Fields of Research (FoR) 2008: | 010299 Applied Mathematics not elsewhere classified |
Fields of Research (FoR) 2020: | 490199 Applied mathematics not elsewhere classified |
Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences |
Socio-Economic Objective (SEO) 2020: | 280118 Expanding knowledge in the mathematical sciences |
Peer Reviewed: | Yes |
HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
Appears in Collections: | Journal Article School of Science and Technology |
Files in This Item:
File | Size | Format |
---|
Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.