Uniqueness of the blow-up boundary solution of logistic equations with absorbtion

Cı̂rstea, Florica-Corina; Rădulescu, Vicenţiu

doi:10.1016/S1631-073X(02)02503-7

Geodesic

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Uniqueness of the blow-up boundary solution of logistic equations with absorbtion
[Unicité de la solution explosant au bord pour équations logistiques avec absorption]

Cı̂rstea, Florica-Corina ¹ ; Rădulescu, Vicenţiu ²

¹ School of Communications and Informatics, Victoria University of Technology, P.O. Box 14428, Melbourne City MC, Victoria 8001, Australia
² Department of Mathematics, University of Craiova, 1100 Craiova, Romania

Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 447-452

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Abstract (VO)
Résumé

Let $Ω$ be a smooth bounded domain in $ℝ^{N}$ . Assume f∈C¹[0,∞) is a non-negative function such that f(u)/u is increasing on (0,∞). Let a be a real number and let b⩾0, $b / \equiv 0$ be a continuous function such that b≡0 on $\partial Ω$ . We study the logistic equation Δu+au=b(x)f(u) in $Ω$ . The special feature of this work is the uniqueness of positive solutions blowing-up on $\partial Ω$ , in a general setting that arises in probability theory.

Soit $Ω$ un domaine borné et régulier de $ℝ^{N}$ . On suppose que f∈C¹[0,∞) est une fonction non-negative telle que f(u)/u soit strictement croissante sur (0,+∞). Soit a un réel et b⩾0, $b / \equiv 0$ une fonction continue sur $\bar{Ω}$ . On étudie l'équation logistique Δu+au=b(x)f(u) sur $Ω$ . Le but de cette Note est de montrer l'unicité de la solution explosant au bord de $Ω$ dans un contexte général, qui apparaı̂t en théorie des probabilités.

Reçu le : 2002-07-01
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02503-7

Affiliations des auteurs :

Cı̂rstea, Florica-Corina ¹ ; Rădulescu, Vicenţiu ²

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Cı̂rstea, Florica-Corina; Rădulescu, Vicenţiu. Uniqueness of the blow-up boundary solution of logistic equations with absorbtion. Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 447-452. doi: 10.1016/S1631-073X(02)02503-7

Cité par Sources :

^☆ The research of F. Cı̂rstea was done under the IPRS Programme funded by the Australian Government through DETYA. V. Rădulescu was supported by the P.I.C.S. Research Programme between France and Romania.