Geodesic
On the Caginalp system with dynamic boundary conditions and singular potentials
Applications of Mathematics, Tome 54 (2009) no. 2, pp. 89-115

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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.
DOI : 10.1007/s10492-009-0008-6
Classification : 35B40, 35B41, 35K55, 35Q53, 80A22
Keywords: Caginalp phase field system; singular potential; dynamic boundary conditions; global existence; global attractor; Łojasiewicz-Simon inequality; convergence to a steady state 
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Cherfils, Laurence; Miranville, Alain. On the Caginalp system with dynamic boundary conditions and singular potentials. Applications of Mathematics, Tome 54 (2009) no. 2, pp. 89-115. doi: 10.1007/s10492-009-0008-6

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