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- W3035502904 abstract "We analyze the EricksenLeslie system equipped with the OseenFrankenergy in three space dimensions. Recently, the author introduced the conceptof dissipative solutions. These solutions show several advantages incomparison to the earlier introduced measure-valued solutions. In thisarticle, we argue that dissipative solutions can be numerically approximatedby a relative simple scheme, which fulfills the norm-restriction on thedirector in every step. We introduce a semi-discrete scheme and derive anapproximated version of the relative-energy inequality for solutions of thisscheme. Passing to the limit in the semi-discretization, we attaindissipative solutions. Additionally, we introduce an optimal control scheme,show the existence of an optimal control and a possible approximationstrategy. We prove that the cost functional is lower semi-continuous withrespect to the convergence of this approximation and argue that an optimalcontrol is attained in the case that there exists a solution admittingadditional regularity." @default.
- W3035502904 created "2020-06-19" @default.
- W3035502904 creator A5074120620 @default.
- W3035502904 date "2018-01-01" @default.
- W3035502904 modified "2023-09-23" @default.
- W3035502904 title "Approximation and optimal control of dissipative solutions to theEricksen-Leslie system" @default.
- W3035502904 doi "https://doi.org/10.34657/2031" @default.
- W3035502904 hasPublicationYear "2018" @default.
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