The phenomenon of quenching in the presence of convection

dc.contributor.advisor Howard A. Levine Park, Sang
dc.contributor.department Mathematics 2018-08-17T07:12:04.000 2020-07-02T06:12:08Z 2020-07-02T06:12:08Z Sun Jan 01 00:00:00 UTC 1989 1989
dc.description.abstract <p>In this paper, we present several results concerning the long time behavior of positive solutions of Burgers' equation u[subscript] t = u[subscript]xx+[epsilon] uu[subscript]x,[epsilon]>0,00,u(x,0) given, subject to one of four pairs of boundary conditions:(UNFORMATTED TABLE OR EQUATION FOLLOWS) (A[subscript]1) u(0,t) = 0,u[subscript] x(1,t) = a(1 - u(1,t))[superscript]-p, t > 0, &(B[subscript]1) u(1,t) = 0,u[subscript]x(0,t) = -a(1 - u(0,t))[superscript]-p, t > 0, &(C[subscript]1) u(0,t) = 0,u[subscript]x(1,t) = a[over] u[superscript]p(1,t), t > 0, & or &(D[subscript]1) u[subscript]x(0,t) = -a[over] u[superscript]p(1,t), u(1,t) = 0, t > 0, & where 0 0. (TABLE/EQUATION ENDS);A complete stability-instability analysis is given. It is shown that for (A) and (B) some solutions quench (reach one in finite time) and that when this happens u[subscript] t(1,t) blows up at the same time. Generalizations replacing uu[subscript] x by (f(u))[subscript]x and (1 - u)[superscript]-p or a[over] u[superscript] p(1,t) by g(u) are discussed with special emphasis on the case g(u) = au[superscript] p - [epsilon][over] 2 u[superscript]2.</p>
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dc.identifier archive/
dc.identifier.articleid 10231
dc.identifier.contextkey 6355677
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/9232
dc.language.iso en
dc.source.bitstream archive/|||Sat Jan 15 02:30:19 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Mathematics
dc.title The phenomenon of quenching in the presence of convection
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 dissertation Doctor of Philosophy
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