Eighth Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 19 (2010), pp. 207-220.

Title: Bounded solutions of nonlinear parabolic equations

Authors: Nsoki Mavinga (Univ. of Rochester, NY, USA)
         Mubenga N. Nkashama (Univ. of Alabama, Birmingham, AL, USA)
 
Abstract: 
 We are concerned with bounded solutions existing for all times for
 nonlinear parabolic equations with possibly nonlinear boundary
 conditions. A counterexample shows that, without an additional
 condition, a (weak) maximum principle does not hold for linear
 problems defined on the entire real line in time. We consider
 solutions bounded for all times and derive a (weak) maximum
 principle which is valid on the entire real line. Using comparison
 techniques, a priori estimates and approximation methods, we
 prove the existence and, in some cases, positivity and uniqueness of
 bounded solutions existing for all times.

Published September 25, 2010.
Math Subject Classifications: 35K55, 35K60.
Key Words: Nonlinear parabolic equations; nonlinear boundary conditions; 
           sub and super-solutions; interpolation inequalities; 
	   a priori estimates; bounded solutions.