THE VOLUME-PRESERVING MOTION BY MEAN CURVATURE AS AN ASYMPTOTIC LIMIT OF REACTION-DIFFUSION EQUATIONS

摘要

The asymptotic behavior of a nonlocal Glnzburg-Landau equation is studied when the small parameter e tends to zero, Here a Lagrange multiplier Ae is introduced into the equation to enforce the conservation of mass. An energy-estimates ap-proach ia used to show that a limiting solution can be characterized by moving interfaces. It ia further shown that the asymptotic limit of solutions of the nonlocal Ginzburg-Landau equation is a weak solution of the nonlocal, maas-preserving mean curvature flow, The weak solutions aro constructed within a framework of the theory of viscosity solutions, In addition, the results describing interactions between the interfaces are obtained.