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Full bounded solutions of nonlinear parabolic equations with nonlinear boundary conditions
by
M. N. Nkashama
University of Alabama at Birmingham
Coauthors: N. Mavinga
We study the existence of bounded solutions existing for all time for nonlinear parabolic equations with nonlinear boundary conditions on a domain that is bounded in space and unbounded in time (the entire real line). We give a counterexample which shows that, without initial condition, a (weak) maximum principle does not hold in general for linear boundary value problems. We use the notion of sub-exponential functions at minus infinity to establish (one-sided) L∞ a priori estimates for solutions to linear boundary value problems, and derive a weak maximum principle which is valid on the entire real line in time. We then take up the case of nonlinear problems with nonlinear boundary conditions. Some examples are given to illustrate the results.
Date received: March 31, 2009
Copyright © 2009 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 # cayt-25.