Asymptotic profile of a radially symmetric solution with transition layers for an unbalanced bistable equation
| dc.contributor.author | Matsuzawa, Hiroshi | |
| dc.date.accessioned | 2021-07-14T15:13:26Z | |
| dc.date.available | 2021-07-14T15:13:26Z | |
| dc.date.issued | 2006-01-11 | |
| dc.description.abstract | In this article, we consider the semilinear elliptic problem -ɛ2 Δu = h(|x|)2 (u - α(|x|)) (1 - u2) in B1(0) with the Neumann boundary condition. The function α is a C1 function satisfying |α(x)| < 1 for x ∈ [0, 1] and α′(0) = 0. In particular we consider the case α(r) = 0 on some interval I ⊂ [0, 1]. The function h is a positive C1 function satisfying h′(0) = 0. We investigate an asymptotic profile of the global minimizer corresponding to the energy functional as ɛ → 0. We use the variational procedure used in [4] with a few modifications prompted by the presence of the function h. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 12 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Matsuzawa, H. (2006). Asymptotic profile of a radially symmetric solution with transition layers for an unbalanced bistable equation. <i>Electronic Journal of Differential Equations, 2006</i>(05), pp. 1-12. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13878 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Transition layer | |
| dc.subject | Allen-Cahn equation | |
| dc.subject | Bistable equation | |
| dc.subject | Unbalanced | |
| dc.title | Asymptotic profile of a radially symmetric solution with transition layers for an unbalanced bistable equation | |
| dc.type | Article |