Global-in-time Gevrey regularity solutions for the functionalized Cahn-Hilliard equation

Kelong Cheng, ,School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China, Cheng Wang, Steven M. Wise, Zixia Yuan, ,Mathematics Department, The University of Massachusetts, North Dartmouth, MA 02747, USA, ,Mathematics Department, The University of Tennessee, Knoxville, TN 37996, USA, ,School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2018 Discrete and Continuous Dynamical Systems. Series S  
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
more » ... imate for the original PDE system indicates a uniform-in-time H 3 bound. Consequently, a global-in-time solution becomes available with Gevrey regularity. 2010 Mathematics Subject Classification. Primary: 35K35, 35K55.
doi:10.3934/dcdss.2020186 fatcat:eqnz7ejwgngudlqratvq3ln26e