NSC Seminar On a phase field model driven by interface area and interface curvature
 Date

20070222 16:30 
20070222 18:00
 Place
 北大電子研N502

Speaker/Organizer
 X.F. Ren (Utah State University)

 It is known that the AllenCahn equation with Neumann boundary condition has no stable nonconstant solution on any convex domain (CastenHolland, Matano). Many modifications have been proposed that yield richer structures of solutions. Examples include a chiral liquid crystal film problem (Selinger, Wang, Bruinsma and Knobler) and a bending membrane problem (Seul and Andelman). In this talk I will discuss an AllenCahn type problem modified by interface curvature, i.e. one adds the interface curvature into the free energy. Every solution of the original AllenCahn problem remains a solution of the new problem. An unstable solution to the old problem becomes stable in the new problem, if the interface curvature part of the free energy is sufficiently large. There also exist solutions to the modified problem that have no counterparts in the original problem. I will show the existence of the so called bubble solutions in this category.
http://wwwnsc.es.hokudai.ac.jp/seminar.html