Article
MSC:
35B40,
35B41,
35K55,
35Q53,
80A22 | MR 2491850 | Zbl 1212.35012 | DOI: 10.1007/s10492-009-0008-6
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Keywords:
Caginalp phase field system; singular potential; dynamic boundary conditions; global existence; global attractor; Łojasiewicz-Simon inequality; convergence to a steady state
Caginalp phase field system; singular potential; dynamic boundary conditions; global existence; global attractor; Łojasiewicz-Simon inequality; convergence to a steady state
Summary:
This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in $H^2$, the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality in order to prove the convergence of solutions to steady states.
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