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dc.contributor.authorMatsuzawa, Hiroshi ( Orcid Icon 0000-0002-2078-1073 )
dc.date.accessioned2021-07-14T15:13:26Z
dc.date.available2021-07-14T15:13:26Z
dc.date.issued2006-01-11
dc.identifier.citationMatsuzawa, H. (2006). Asymptotic profile of a radially symmetric solution with transition layers for an unbalanced bistable equation. Electronic Journal of Differential Equations, 2006(05), pp. 1-12.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13878
dc.description.abstract

In this article, we consider the semilinear elliptic problem

2 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.formatText
dc.format.extent12 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectTransition layeren_US
dc.subjectAllen-Cahn equationen_US
dc.subjectBistable equationen_US
dc.subjectUnbalanceden_US
dc.titleAsymptotic profile of a radially symmetric solution with transition layers for an unbalanced bistable equationen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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