Asymptotic analysis for elliptic equations with Robin boundary condition

Article type: Research Article

Authors: Kim, Junghwa^{; *}

Affiliations: Department of Mathematics, University of Louisville, Louisville, KY 40292, USA. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We investigate the boundary layers of a singularly perturbed reaction-diffusion equation in a 3D channel domain. The equation is supplemented with a Robin boundary condition especially when the smooth function on the boundary, appearing in the Robin boundary condition, depends on the perturbation parameter. By constructing an explicit function, called corrector, which describes behavior of the perturbed solution near the boundary, we obtain an asymptotic expansion of the perturbed solution as the sum of the corresponding limit solution and the corrector, and show the convergence in L2 of the perturbed solution to the limit solution as the perturbation parameter tends to zero.

Keywords: Boundary layers, singular perturbations, Robin boundary condition

DOI: 10.3233/ASY-201618

Journal: Asymptotic Analysis, vol. 122, no. 3-4, pp. 257-269, 2021