seminar

In this talk, a ternary Cahn-Hilliard system with a Flory-Huggins-deGennesfree energy potential is considered, in which the key diffculty has alwaysbeen associated with the singularity ofthe logarithmic terms. An energy stablefnite difference scheme based on the convex splitting method, whichimplicitly treats the logarithmic terms, is proposed and analyzed in this talkWe provide a theoretical justification that this numerical scheme has a pair ofunique solutions, such that the positivity is always preserved for all thesingular terms, i.e., not only two phase variables are always between 0 and 1.but also the sum of two phase variables is between 0 and 1, at a point-wiselevel. As a result, the numerical scheme is proven to be well-defined, and theunique solvability and energy stability could be established with the help ofconvexity analysis. In addition, an optimal rate convergence analysis could beappropriately established. Some numerical results are also presented.