Special Session 18: Advanced methodologies in mathematical materials science and biology

Global existence of solutions to a singular nonlocal phase field system with inertial term

Shunsuke Kurima
Department of Mathematics, Tokyo University of Science
Japan
Co-Author(s):    
Abstract:
This talk deals with a nonlocal phase field system with inertial term. Colli--Colturato (2018) have established existence of solutions to a phase field system related to the entropy balance. Also, Colli--Grasselli--Ito (2002) have proved existence of solutions to a parabolic-hyperbolic Penrose--Fife phase field system. However, singular nonlocal phase field systems with inertial term seem to be not studied yet. The present work asserts that we can derive existence of solutions to a singular nonlocal phase field system with inertial term.