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

Published online by Cambridge University Press:  25 February 2013

SAMI BARAKET
Affiliation:
Department of Mathematics, College of Science King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia e-mail: sbaraket@ksu.edu.sa
TAIEB OUNI
Affiliation:
Département de Mathématiques, Faculté des Sciences de TunisCampus Universitaire, 2092 Tunis, Tunisia e-mail: Taieb.Ouni@fst.rnu.tn
Corresponding
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Abstract

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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

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