We introduce several notions of generalised principal eigenvalue for a linear elliptic operator on a general unbounded domain, under boundary condition of the oblique derivative type. We employ these notions in the stability analysis of semilinear problems. Some of the properties we derive are new even in the Dirichlet or in the whole space cases. As an application, we show the validity of the hair-trigger effect for the Fisher-KPP equation on general, uniformly smooth domains.
Stability analysis for semilinear parabolic problems in general unbounded domains / Rossi, L.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 279:7(2020). [10.1016/j.jfa.2020.108657]
Stability analysis for semilinear parabolic problems in general unbounded domains
Rossi L.
2020
Abstract
We introduce several notions of generalised principal eigenvalue for a linear elliptic operator on a general unbounded domain, under boundary condition of the oblique derivative type. We employ these notions in the stability analysis of semilinear problems. Some of the properties we derive are new even in the Dirichlet or in the whole space cases. As an application, we show the validity of the hair-trigger effect for the Fisher-KPP equation on general, uniformly smooth domains.| File | Dimensione | Formato | |
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