Publication Date:
2004
Citation:
Universal attractor for some singular phase
transition systems / E. Rocca, G. Schimperna. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - 192:3-4(2004), pp. 279-307. [10.1016/j.physd.2004.01.024]
abstract:
A singular parabolic system describing the thermal diffusion in a substance possibly subject to a phase transition is
introduced. The physical process is described by the variables ϑ (absolute temperature) and χ (order parameter). The latter
may have, or not, conserved total mass with respect to time. In both cases, after recalling and sometimes improving some
known well-posedness results, the long-time behavior of the system is studied. It is shown that the process is dissipative and
the compact universal attractor is constructed. It turns out to attract the trajectories of the system in a rather strong metric
which is strictly linked to the constraints imposed to both variables. The techniques used in the proofs seem likely to be
applied to other types of evolution systems containing maximal monotone nonlinearities.
introduced. The physical process is described by the variables ϑ (absolute temperature) and χ (order parameter). The latter
may have, or not, conserved total mass with respect to time. In both cases, after recalling and sometimes improving some
known well-posedness results, the long-time behavior of the system is studied. It is shown that the process is dissipative and
the compact universal attractor is constructed. It turns out to attract the trajectories of the system in a rather strong metric
which is strictly linked to the constraints imposed to both variables. The techniques used in the proofs seem likely to be
applied to other types of evolution systems containing maximal monotone nonlinearities.
IRIS type:
01 - Articolo su periodico
List of contributors:
E. Rocca, G. Schimperna
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