Asymptotic behavior of the solutions to a family of PDE's arising from the chemotaxis equations of Keller and Segal

dc.contributor.advisor Howard Levine
dc.contributor.advisor Elgin Johnston
dc.contributor.advisor Leslie Hogben
dc.contributor.author Halverson, Matthew
dc.contributor.department Mathematics
dc.date 2018-08-22T20:26:39.000
dc.date.accessioned 2020-06-30T07:46:12Z
dc.date.available 2020-06-30T07:46:12Z
dc.date.copyright Tue Jan 01 00:00:00 UTC 2008
dc.date.issued 2008-01-01
dc.description.abstract <p>The system ut = uxx - (uvx)x, vt = u - Av is considered where A is a non-negative, self-adjoint operator which commutes with the Laplacian. The operator is considered to have eigenvalues lambda n = nrholambda1, and the system is considered on [0,1] x [0,T] with homogeneous Neumann boundary conditions. The operators which lead to global solutions and those that lead to solutions which blow up in finite time are considered as a function of rho, using an application of the methods of Hillen and Potapov [Math. Methods Appl. Sci., 27 (2004), pp. 1783-1801] to analyze the global case and those of Halverson, Levine, and Renclawowicz [Siam J. Appl. Math., 65 (2004), pp. 336--360; 66 (2005), pp. 361--364] to analyze the finite time blowup case. Some numerical results are provided to back up the analysis. Some questions and directions for future study are posed.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/15654/
dc.identifier.articleid 16653
dc.identifier.contextkey 7037882
dc.identifier.doi https://doi.org/10.31274/rtd-180813-16867
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/15654
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/69308
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/15654/3307081.PDF|||Fri Jan 14 20:44:28 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Mathematics;
dc.title Asymptotic behavior of the solutions to a family of PDE's arising from the chemotaxis equations of Keller and Segal
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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