Abstract
The existence and uniqueness of Gevrey regularity solutions for the functionalized Cahn-Hilliard (FCH) and Cahn-Hilliard-Willmore (CHW) equations are established. The energy dissipation law yields a uniform-in-time H-2 bound of the solution, and the polynomial patterns of the nonlinear terms enable one to derive a local-in-time solution with Gevrey regularity. A careful calculation reveals that the existence time interval length depends on the H-3 norm of the initial data. A further detailed estimate for the original PDE system indicates a uniform-in-time H-3 bound. Consequently, a global-in-time solution becomes available with Gevrey regularity.