scholarly journals FINITE-DIMENSIONAL GLOBAL ATTRACTOR FOR A NONLOCAL PHASE-FIELD SYSTEM

2012 ◽  
Author(s):  
Maurizio Grasselli
Keyword(s):  
Global Attractor ◽  
Phase Field ◽  
Energy Balance Equation ◽  
Absorbing Set ◽  
Field System ◽  
Finite Dimensional ◽  
Long Range Interactions ◽  
Bounded Absorbing Set ◽  
Singular Configuration ◽  
Phase Field System

We analyze a phase-field system where the energy balance equation is linearly coupled with a nonlinear and nonlocal ODE for the order parameter . The latter equation is characterized by a space convolution term which models long-range interactions and a singular configuration potential that forces to take values in the interval (􀀀1; 1). We prove that the corresponding dynamical system is dissipative, i.e., it has a bounded absorbing set in a suitable phase space. Then we establish the existence of a finite-dimensional global attractor.

scholarly journals Global attractor for a parabolic-hyperbolic Penrose-Fife phase field system

2006 ◽  
Vol 15 (4) ◽  
pp. 1193-1214
Author(s):  
Elisabetta Rocca ◽  
◽  
Giulio Schimperna ◽  
Keyword(s):  
Global Attractor ◽  
Phase Field ◽  
Field System ◽  
Phase Field System

Study of the dissipativity, global attractor and exponential attractor for a hyperbolic relaxation of the Caginalp phase-field system with singular nonlinear terms

2020 ◽  
pp. 1-28
Author(s):  
Urbain Cyriaque Mavoungou ◽  
Narcisse Batangouna ◽  
Franck Davhys Reval Langa ◽  
Daniel Moukoko ◽  
Macaire Batchi
Keyword(s):  
Boundary Condition ◽  
Global Attractor ◽  
Phase Field ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Exponential Attractor ◽  
Field System ◽  
Phase Field System

In this paper, we study of the dissipativity, global attractor and exponential attractor for a hyperbolic relaxation of the Caginalp phase-field system with singular nonlinear terms, with initial and homogenous Dirichlet boundary condition.

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