FLAT BLOW-UP SOLUTIONS FOR THE COMPLEX GINZBURG LANDAU EQUATION
Solution explosive plate pour l'équation complexe de Ginzburg Landau
Résumé
In this paper, we consider the complex Ginzburg Landau equation ut=(1+iβ)Δu+(1+iδ)|u|p−1u−αu where β, δ, α are in R. The study aims to investigate the finite time blowup phenomenon. In particular, for fixed β P R, the existence of finite time blowup solutions for an arbitrary large |δ| is still unknown. Especially, Popp et al [24] formally conjectured that there is no blowup (collapse) in such case. In this work, considered as a breakthrough, we give a counter example to this conjecture. We show the existence of blowup solutions in one dimension with δ arbitrarily given and β " 0. The novelty is based on two main contributions: an investigation of a new blowup scaling (flat blowup regime) and a suitable modulation.
Mots clés
2010 Mathematics Subject Classification. Primary: 35K05 35B40
Secondary: 35K55 35K57 Finite time blowup Blowup asymptotic behavior Stability Complex Ginzburg-Landau equation. August 28 2023
2010 Mathematics Subject Classification. Primary: 35K05
35B40
Secondary: 35K55
35K57 Finite time blowup
Blowup asymptotic behavior
Stability
Complex Ginzburg-Landau equation. August 28
2023
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