Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions

This paper deals with the longtime behavior of the Caginalp phase-field system with coupled dynamic boundary conditions on both state variables.We prove that the system generates a dissipative semigroup in a suitable phase-spaceand possesses the finite-dimensional smooth global attractor and an exponential attractor.This paper deals with the longtime behavior of the Caginalp phasefield system with coupled dynamic boundary conditions on both state variables. We prove that the system generates a dissipative semigroup in a suitable phasespace and possesses the finite-dimensional smooth global attractor and an exponential attractor