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dc.contributor.authorBellout, Hamid
dc.contributor.authorBenachour, Said
dc.contributor.authorTiti, Edriss S.
dc.date.accessioned2013-02-06T16:07:56Z
dc.date.available2013-02-06T16:07:56Z
dc.date.issued2003
dc.identifier.citationBellout, H, S. Benachour and E.S. Titi, "Finite-time singularity versus global regularity for hyper-viscous Hamilton-Jacobi-like equations" Nonlinearity 16 (November 2003) 1967-1989.en_US
dc.identifier.issn0951-7715
dc.identifier.urihttp://commons.lib.niu.edu/handle/10843/13409
dc.identifier.urihttp://hdl.handle.net/10843/13409
dc.description.abstractThe global regularity for the two- and three-dimensional Kuramoto-Sivashinsky equations is one of the major open questions in nonlinear analysis. Inspired by this question, we introduce in this paper and family of hyper-viscous Hamilton-Jacobi-like equations parametrized by the exponent in the nonlinear term, p, where in the case of the usual Hamilton-Jacobi nonlinearity, p = 2. Under certain conditions on the exponent p we prove the short-time existence of weak and strong solutions to this family of equations. We also show the uniqueness of strong solutions. Moreover, we prove the blow-up in finite time of certain solutions to this family of equations when the exponent p > 2. Furthermore, we discuss the difference in the formation and structure of the singularity between the viscous and hyper-viscous versions of this type of equation.en_US
dc.language.isoen_USen_US
dc.publisherInstitute of Physicsen_US
dc.subjectKuramoto-Sivashinsky equationsen_US
dc.subjectHamilton-Jacoby nonlinearityen_US
dc.titleFinite-time singularity versus global regularity for hyper-viscous Hamilton-Jacobi-like equationsen_US
dc.typeArticleen_US
dc.contributor.departmentDepartment of Mathematical Sciences


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