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dc.contributor.authorCorrêa, Wellington José
dc.contributor.authorÖzsarı, Türker
dc.date.accessioned2020-01-16T07:15:51Z
dc.date.available2020-01-16T07:15:51Z
dc.date.issued2018-06en_US
dc.identifier.citationCorrêa, W. J., and Özsarı, T. (2018). Complex Ginzburg–Landau equations with dynamic boundary conditions. Nonlinear Analysis: Real World Applications, 41, 607-641. doi:10.1016/j.nonrwa.2017.12.001en_US
dc.identifier.issn1468-1218
dc.identifier.urihttps://doi.org/10.1016/j.nonrwa.2017.12.001
dc.identifier.urihttps://hdl.handle.net/11147/7588
dc.description.abstractThe initial-dynamic boundary value problem (idbvp) for the complex Ginzburg–Landau equation (CGLE) on bounded domains of RN is studied by converting the given mathematical model into a Wentzell initial–boundary value problem (ibvp). First, the corresponding linear homogeneous idbvp is considered. Secondly, the forced linear idbvp with both interior and boundary forcings is studied. Then, the nonlinear idbvp with Lipschitz nonlinearity in the interior and monotone nonlinearity on the boundary is analyzed. The local well-posedness of the idbvp for the CGLE with power type nonlinearities is obtained via a contraction mapping argument. Global well-posedness for strong solutions is shown. Global existence and uniqueness of weak solutions are proven. Smoothing effect of the corresponding evolution operator is proved. This helps to get better well-posedness results than the known results on idbvp for nonlinear Schrödinger equations (NLS). An interesting result of this paper is proving that solutions of NLS subject to dynamic boundary conditions can be obtained as inviscid limits of the solutions of the CGLE subject to same type of boundary conditions. Finally, long time behavior of solutions is characterized and exponential decay rates are obtained at the energy level by using control theoretic tools.en_US
dc.description.sponsorshipTUBITAK (115F055)en_US
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.relation.isversionof10.1016/j.nonrwa.2017.12.001en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectInviscid limitsen_US
dc.subjectDynamic boundary conditionsen_US
dc.subjectNonlinear equationsen_US
dc.subjectLandau equationen_US
dc.titleComplex Ginzburg–Landau equations with dynamic boundary conditionsen_US
dc.typearticleen_US
dc.contributor.authorID0000-0003-4240-5252en_US
dc.contributor.iztechauthorÖzsarı, Türker
dc.relation.journalNonlinear Analysis: Real World Applicationsen_US
dc.contributor.departmentIzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume41en_US
dc.identifier.startpage607en_US
dc.identifier.endpage641en_US
dc.identifier.wosWOS:000424721700031
dc.identifier.scopusSCOPUS:2-s2.0-85038826755
dc.relation.tubitakinfo:eu-repo/grantAgreement/TUBITAK/MFAG/115F055
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US


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