Singular Limits for 4-Dimensional General Stationary Q-Kuramoto-Sivashinsky Equation (Q-Kse) with Exponential Nonlinearity

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.