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Seventh Mississippi State - UAB Conference on Differential Equations & Computational Simulations
November 1-3, 2007
Doubletree Hotel
Birmingham, AL, USA

Organizers
Mississippi State University & University of Alabama - Birmingham

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Bounded Solutions of Nonlinear Parabolic Systems
by
Nsoki Mavinga
University of Alabama at Birmingham
Coauthors: Dr. Mubenga Nkashama

We consider coupled systems of two nonlinear parabolic equations on a domain which is bounded in space and unbounded in time (namely the entire real line). We establish the existence of bounded solutions existing for all time by using a combination of a priori estimates, comparison techniques, nonlinear approximations, embedding of function spaces, and Gagliardo-Nirenberg type interpolation inequalities which we derive. Additional conditions ensure uniqueness or multiplicity of solutions. Some examples will be given to illustrate the results.

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Date received: August 31, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cauf-79.