%0 Journal Article
%T Bounded solutions of nonlinear parabolic equations
%A Nsoki Mavinga
%A Mubenga N. Nkashama
%J Electronic Journal of Differential Equations
%D 2010
%I Texas State University
%X 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.
%K Nonlinear parabolic equations
%K nonlinear boundary conditions
%K sub and super-solutions
%K interpolation inequalities
%K a priori estimates
%K bounded solutions
%U http://ejde.math.txstate.edu/conf-proc/19/m2/abstr.html