Asymptotic behavior of a nonisothermal viscous Cahn-Hilliard equation with inertial term
| dc.creator | Grasselli, Maurizio | |
| dc.creator | Petzeltova, Hana | |
| dc.creator | Schimperna, Giulio | |
| dc.date | 2006-11-06 | |
| dc.date.accessioned | 2026-07-07T07:32:33Z | |
| dc.date.available | 2026-07-07T07:32:33Z | |
| dc.description | We consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an inertial term $χ_{tt}$, $χ$ being the order parameter, which is linearly coupled with an evolution equation for the (relative) temperature $\teta$. The latter can be of hyperbolic type if the Cattaneo-Maxwell heat conduction law is assumed. The state variables and the chemical potential are subject to the homogeneous Neumann boundary conditions. We first provide conditions which ensure the well-posedness of the initial and boundary value problem. Then, we prove that the corresponding dynamical system is dissipative and possesses a global attractor. Moreover, assuming that the nonlinear potential is real analytic, we establish that each trajectory converges to a single steady state by using a suitable version of the Lojasiewicz-Simon inequality. We also obtain an estimate of the decay rate to equilibrium. | |
| dc.identifier | https://arxiv.org/abs/math/0611134 | |
| dc.identifier | http://arxiv.org/abs/math/0611134 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119151 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Dynamical Systems | |
| dc.subject | 35B40, 35B41, 35R35, 80A22 | |
| dc.title | Asymptotic behavior of a nonisothermal viscous Cahn-Hilliard equation with inertial term | |
| dc.type | text |