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Convergence of Solutions to a Convective Cahn–Hilliard-Type Equation of the Sixth Order in Case of Small Deposition Rates

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dc.abstract.enWe show stabilization of solutions to the sixth-order convective Cahn–Hilliard equation. The problem has the structure of a gradient flow perturbed by a quadratic destabilizing term with coefficient . Through application of an abstract result by Carvalho, Langa, and Robinson we show that for small the equation has the structure of gradient flow in a weak sense. On the way we prove a kind of Liouville theorem for eternal solutions to parabolic problems. Finally, the desired stabilization follows from a powerful theorem due to Hale and Raugel.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorWheeler, Glen
dc.contributor.authorRybka, Piotr
dc.date.accessioned2024-01-24T20:47:49Z
dc.date.available2024-01-24T20:47:49Z
dc.date.issued2023
dc.description.financePublikacja bezkosztowa
dc.description.number5
dc.description.volume55
dc.identifier.doi10.1137/22M1540429
dc.identifier.issn0036-1410
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/103724
dc.identifier.weblinkhttp://dx.doi.org/10.1137/22m1540429
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofSIAM Journal on Mathematical Analysis
dc.relation.pages5823-5861
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enstabilization of solutions
dc.subject.engradient-type systems
dc.subject.enconvective Cahn–Hilliard-type equation
dc.titleConvergence of Solutions to a Convective Cahn–Hilliard-Type Equation of the Sixth Order in Case of Small Deposition Rates
dc.typeJournalArticle
dspace.entity.typePublication