Calculus of Variations and Geometric Measure Theory

M. Colturato

Well-posedness and longtime behavior for a singular phase field system with perturbed phase dynamics

created by michele on 06 Aug 2018
modified on 04 May 2020


Published Paper

Inserted: 6 aug 2018
Last Updated: 4 may 2020

Journal: Evol. Equ. Control Theory
Volume: 7
Pages: 28
Year: 2018


We consider a singular phase field system located in a smooth bounded domain. In the entropy balance equation appears a logarithmic nonlinearity. The second equation of the system, deduced from a balance law for the microscopic forces that are responsible for the phase transition process, is perturbed by an additional term involving a possibly nonlocal maximal monotone operator and arising from a class of sliding mode control problems. We prove existence and uniqueness of the solution for this resulting highly nonlinear system. Moreover, under further assumptions, the longtime behavior of the solution is investigated.