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Sami Baraket, Imen Bazarbacha, Saber Kharrati and Taieb Ouni

Abstract

We study existence of solutions with singular limits for a two-dimensional semilinear elliptic problem with exponential dominated nonlinearity and a quadratic convection non linear gradient term, imposing Dirichlet boundary condition. This paper extends previous results obtained in [1], [3], [4] and some references therein for related issues.

Open access

Taieb Ouni, Sami Baraket and Moufida Khtaifi

Abstract

Let Ω be a bounded domain in with smooth boundary, and let 𝓧1; 𝓧2; · · ·, 𝓧m be points in Ω. We are concerned with the singular stationary non-homogenous q-Kuramoto-Sivashinsky eaquation (q-KSE:

where we use some nonlinear domain decomposition method to give a suficient condition to have a positive weak solution u in Ω under the physical Dirichlet-like boundary conditions , which is singular at each 𝓧i as the parameters λ, ϒ and ρ tend to 0 and where q ∈ [1, 4] is a real number.