Catenoidal layers for the Allen-Cahn equation in bounded domains

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43930420" target="_blank" >RIV/49777513:23520/17:43930420 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007/s11401-016-1062-5" target="_blank" >http://link.springer.com/article/10.1007/s11401-016-1062-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11401-016-1062-5" target="_blank" >10.1007/s11401-016-1062-5</a>

Result language
angličtina
Original language name
Catenoidal layers for the Allen-Cahn equation in bounded domains
Original language description
This article presents a new family of solutions to the singularly perturbed Allen-Cahn equation α2Δu + u(1 − u2) = 0 in a smooth bounded domain Ω ⊂ R3, with Neumann boundary condition and α > 0 a small parameter. These solutions have the property that as α → 0, their level sets collapse onto a bounded portion of a complete embedded minimal surface with finite total curvature intersecting ∂Ω orthogonally and that is non-degenerate respect to ∂Ω. The authors provide explicit examples of surfaces to which the result applies.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA13-00863S" target="_blank" >GA13-00863S: Semilinear and Quasilinear Differential Equations: Existence and Multiplicity Results</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
C - Předmět řešení projektu podléhá obchodnímu tajemství (§ 504 Občanského zákoníku), ale název projektu, cíle projektu a u ukončeného nebo zastaveného projektu zhodnocení výsledku řešení projektu (údaje P03, P04, P15, P19, P29, PN8) dodané do CEP, jsou upraveny tak, aby byly zveřejnitelné.

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