Finite-dimensional global attractor for a nonlocal phase-field system
Abstract
We analyze a phase-field system where the energy balance equation is linearly coupled with a nonlinear and nonlocal ODE for the order parameter $\chi$. The latter equation is characterized by a space convolution term which models particle interaction and a singular configuration potential that forces $\chi$ to take values in $(-1,1)$. We prove that the corresponding dynamical system has a bounded absorbing set in a suitable phase space. Then we establish the existence of a finite-dimensional global attractor.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2011
- DOI:
- 10.48550/arXiv.1108.0314
- arXiv:
- arXiv:1108.0314
- Bibcode:
- 2011arXiv1108.0314G
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematics - Analysis of PDEs;
- 35B41;
- 35Q99;
- 80A22
- E-Print:
- 14 pages