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Article Dans Une Revue Communications in Partial Differential Equations Année : 2021

Moving planes for domain walls in a coupled system

Résumé

The system leading to phase segregation in two-component Bose-Einstein condensates can be generalized to hyperfine spin states with a Rabi term coupling. This leads to domain wall solutions having a monotone structure for a non-cooperative system. We use the moving plane method to prove mono-tonicity and one-dimensionality of the phase transition solutions. This relies on totally new estimates for a type of system for which no Maximum Principle a priori holds. We also derive that one dimensional solutions are unique up to translations. When the Rabi coefficient is large, we prove that no non-constant solutions can exist.
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Dates et versions

hal-02190665 , version 1 (22-07-2019)
hal-02190665 , version 2 (19-11-2022)

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Amandine Aftalion, Alberto Farina, Luc Nguyen. Moving planes for domain walls in a coupled system. Communications in Partial Differential Equations, 2021, 46 (8), pp.1410-1439. ⟨10.1080/03605302.2021.1881112⟩. ⟨hal-02190665v2⟩
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