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

<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>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

dissertation

Department dc:contributor.department

Department of Mathematics

Year dc:date.issued

2008

Author dc:creator

• Halverson, Matthew

Advisors dc:contributor.advisor

• Howard Levine
• Elgin Johnston
• Leslie Hogben

Language dc:language.iso

en

DOI

https://doi.org/10.31274/rtd-180813-16867

Identifier

archive/lib.dr.iastate.edu/rtd/15654/

OAI identifier oai:identifier

oai:dr.lib.iastate.edu:20.500.12876/69308