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The existence and uniqueness of Gevrey regularity solution for a class of nonlinear

bistable gradient flows, with the energy decomposed into purely convex and concave parts,

such as epitaxial thin film growth and square phase field crystal models, are discussed in this talk.

The polynomial pattern of the nonlinear terms in the chemical potential enables one to derive a

local in time solution with Gevrey regularity, with the existence time interval length dependent

on certain functional norms of the initial data. Moreover, a detailed Sobolev estimate for the gradient

equations results in a uniform in time bound, which in turn establishes a global in

time solution with Gevrey regularity. An extension to a system of gradient flows,

such as the three-component Cahn-Hilliard equations, is also addressed in this talk.