Boundary layer solutions to problems with infinite-dimensional singular and regular perturbations
The authors prove existence, local uniqueness and asymptotic estimates for boundary layer solutions to singularly perturbed equations of the type \[ (\varepsilon (x))^{2}u'(x))'=f(x,u(x))+g(x,u (x),\varepsilon(x)u'(x)),\quad 0<x<1 \] with Dirichlet and Neumann boundary conditions. Here, the functions \(\varepsilon \) and \(g\) are small and regarded as singular and regular functional perturbation parameters.
space depending small diffusion coefficient
scientific article; zbMATH DE number 5382300