SINGULAR LIMITS FOR 2-DIMENSIONAL ELLIPTIC PROBLEMS INVOLVING EXPONENTIAL NONLINEARITIES WITH SUB-QUADRATIC CONVECTION TERM

BARAKET, SAMI ; OUNI, TAIEB

Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 537-557

Résumé

Let Ω be a bounded domain with smooth boundary in R2, q∈[1,2) and x1, x2,. . .,xm ∈ Ω. In this paper we are concerned with the following type of problem:\[ -\Delta u-\lambda|\nabla u|^q = \rho^{2}e^{u}, \]with u = 0 on ∂ Ω. We use some nonlinear domain decomposition method to construct a positive weak solution vρ,λ in Ω, which tends to a singular function at each xi as the parameters ρ and λ tend to 0 independently.

Détail

DOI : 10.1017/S0017089512000729

Mots-clés : 35J60, 53C21, 58J05

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