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- W2041503996 abstract "We consider a phase-field system of Caginalp type on athree-dimensional bounded domain. The order parameter $psi $fulfills a dynamic boundary condition, while the (relative)temperature $theta $ is subject to a boundary condition ofDirichlet, Neumann, Robin or Wentzell type. The correspondingclass of initial and boundary value problems has already beenstudied by the authors, proving well-posedness results and theexistence of global as well as exponential attractors. Here weintend to show first that the previous analysis can be redone forlarger phase-spaces, provided that the bulk potential has afourth-order growth at most whereas the boundary potential has anarbitrary polynomial growth. Moreover, assuming the potentials tobe real analytic, we demonstrate that eachtrajectory converges to a single equilibrium by means of a Łojasiewicz-Simon type inequality. We also obtain a convergencerate estimate." @default.
- W2041503996 created "2016-06-24" @default.
- W2041503996 creator A5004351524 @default.
- W2041503996 creator A5054462385 @default.
- W2041503996 date "2009-01-01" @default.
- W2041503996 modified "2023-09-24" @default.
- W2041503996 title "On the asymptotic behavior of the Caginalp system with dynamic boundary conditions" @default.
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- W2041503996 doi "https://doi.org/10.3934/cpaa.2009.8.689" @default.
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