Abstract
In this paper we formulate a boundary layer approximation for an Allen–Cahn-type equation involving a small parameter \({\varepsilon}\) . Here, \({\varepsilon}\) is related to the thickness of the boundary layer and we are interested in the limit \({\varepsilon \to 0}\) in order to derive nontrivial boundary conditions. The evolution of the system is written as an energy balance formulation of the L2-gradient flow with the corresponding Allen–Cahn energy functional. By transforming the boundary layer to a fixed domain we show the convergence of the solutions to a solution of a limit system. This is done by using concepts related to Γ- and Mosco convergence. By considering different scalings in the boundary layer we obtain different boundary conditions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Nonlinear Differential Equations and Applications NoDEA
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
