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Non-Linear Elliptic Eigenvalue Problems, with Applications to Thermal Combustion

dc.contributor.authorAptekar-Fradkin, Larissa Ju
dc.date.accessioned2008-08-20T03:40:02Z
dc.date.accessioned2022-11-02T02:18:02Z
dc.date.available2008-08-20T03:40:02Z
dc.date.available2022-11-02T02:18:02Z
dc.date.copyright1977
dc.date.issued1977
dc.description.abstractA study is made of the equations of combustion for a steady – state thermal regime with non-linear (with temperature) heat generation in the material with a linearized radiation condition on the boundary. A mathematical model is discussed which gives rise to a (mildly) non-linear elliptic boundary value problem. The nature of the solution set of a class of non-linear elliptic boundary value problems as dependent on the form of the nonlinearity is studied. The conditions are discussed which determine the topological properties of the spectrum and for which there exist the critical points in spectrum The stability properties of the supremum of spectrum (under small perturbations of the operators involved) are studied. The definition of the critical explosion parameter is given and the question of its existence is discussed. The variational problem associated with the non-linear eigenvalue problem is studied, so that necessary conditions are established for the Wake and Rayner method of computation of the critical explosion parameter to be used in the general case. As a result, the mathematical theory of thermal combustion is developed - under a plausible heuristic hypothesis - in which the criticality parameters possess essentially the same properties as those in the Semenov qualitative theory of thermal combustion. The mathematical Justification of the widely used Frank - Kamenetskii approximation is obtained in the framework of this theory. Most of the results are extended to a broad class of problems with (mild) nonlinearities in, boundary conditions.en_NZ
dc.formatpdfen_NZ
dc.identifier.urihttps://ir.wgtn.ac.nz/handle/123456789/28536
dc.languageen_NZ
dc.language.isoen_NZ
dc.publisherTe Herenga Waka—Victoria University of Wellingtonen_NZ
dc.rights.holderAll rights, except those explicitly waived, are held by the Authoren_NZ
dc.rights.licenseAuthor Retains Copyrighten_NZ
dc.rights.urihttps://www.wgtn.ac.nz/library/about-us/policies-and-strategies/copyright-for-the-researcharchive
dc.subjectBoundary value problemsen_NZ
dc.subjectNonlinear differential equationsen_NZ
dc.subjectCombustionen_NZ
dc.titleNon-Linear Elliptic Eigenvalue Problems, with Applications to Thermal Combustionen_NZ
dc.typeTexten_NZ
thesis.degree.disciplineMathematicsen_NZ
thesis.degree.grantorTe Herenga Waka—Victoria University of Wellingtonen_NZ
thesis.degree.levelDoctoralen_NZ
thesis.degree.nameDoctor of Philosophyen_NZ
vuwschema.type.vuwAwarded Doctoral Thesisen_NZ

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