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- ItemExistence and asymptotic stability of a periodic solution with boundary layers of reaction-diffusion equations with singularly perturbed Neumann boundary conditions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Butuzov, Valentin F.; Nefedov, Nikolai N.; Recke, Lutz; Schneider, Klaus R.We consider singularly perturbed reaction-diffusion equations with singularly perturbed Neumann boundary conditions. We establish the existence of a time-periodic solution u(x; t; epsilon) with boundary layers and derive conditions for their asymptotic stability The boundary layer part of u(x; t; ") is of order one, which distinguishes our case from the case of regularly perturbed Neumann boundary conditions, where the boundary layer is of order epsilon.