Bounded Solutions of Nonlinear parabolic Systems
by
Nsoki Mavinga
University of Alabama at Birmingham
Coauthors: Dr. M. 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.

Date received: August 31, 2007