Abstract
In this paper, we demonstrate, through asymptotic expansions, the convergence of a phase field formulation to model surfaces minimizing the mean curvature energy with volume and surface area constraints. Under the assumption of the existence of a smooth limiting surface, it is shown that the interface of a phase field, which is a critical point of the elastic bending energy, converges to a critical point of the surface energy. Further, the elastic bending energy of the phase field converges to the surface energy and the Lagrange multipliers associated with the volume and surface area constraints remain uniformly bounded. This paper is a first step to analytically justify the numerical simulations performed by Du, Liu and Wang in 2004 to model equilibrium configurations of vesicle membranes.
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 callDisclaimer: 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.
