k-ended O(m) x O(n) invariant solutions to the Allen-Cahn equation with infinite Morse index

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43966212" target="_blank" >RIV/49777513:23520/22:43966212 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022123622001811?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022123622001811?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2022.109561" target="_blank" >10.1016/j.jfa.2022.109561</a>

Result language
angličtina
Original language name
k-ended O(m) x O(n) invariant solutions to the Allen-Cahn equation with infinite Morse index
Original language description
In this work we study existence, asymptotic behaviour and stability properties of O(m) ×O(n)-invariant solutions of the Allen-Cahn equation Δu +u(1 −u2) =0 in Rm×Rn with m, n ≥2 and m +n ≥8. We exhibit four families of solutions whose nodal sets are smooth logarithmic corrections of the Lawson cone and with infinite Morse index. This work complements earlier studies started by Pacard and Wei and by Agudelo, Kowalczykand Rizzi.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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