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- W2525706249 abstract "We propose a mathematical analysis of the Swift-Hohenberg equation arising from the phase field theory to model the transition from an unstable to a (meta)stable state. We also consider a recent generalization of the original equation, obtained by introducing an inertial term, to predict fast degrees of freedom in the system. We formulate and prove well-posedness results of the concerned models. Afterwards, we analyse the long-time behavior in terms of global and exponential attractors. Finally, by reading the inertial term as a singular perturbation of the Swift-Hohenberg equation, we construct a family of exponential attractors which is Holder continuous with respect to the perturbative parameter of the system." @default.
- W2525706249 created "2016-10-07" @default.
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- W2525706249 date "2015-12-01" @default.
- W2525706249 modified "2023-10-14" @default.
- W2525706249 title "On the Swift-Hohenberg equation with slow and fast dynamics: well-posedness and long-time behavior" @default.
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- W2525706249 doi "https://doi.org/10.3934/cpaa.2016.15.219" @default.
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