Existence and regularity of the solution of the triplet phase separation equation

In the report， the existence and uniqueness of the solution of the triplet phase separation equation were studied. Firstly， Galerkin method was used to propose the existence theorem of the solution of a class of abstract equations； secondly， the operators were introduced， the conditions required by the theorem were verified， and the existence of the solution was obtained； thirdly， the uniqueness of the understanding was proved by the spatial interpolation inequality and the related properties of the symmetry operator； finally， the iterative process of the regularity estimation of linear semigroups was used to improve the regularity of the solution.