Variational and Topological Methods: Theory, Applications, 
Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 197--221.

Title: Strong bounded solutions for nonlinear parabolic systems

Authors: Nsoki Mavinga  (Swarthmore College, PA 19081, USA)
         Mubenga N. Nkashama (Univ. of Alabama at Birmingham, AL, USA)
 
Abstract: 
  In  this article we  study the existence of  strong bounded solutions for
  nonlinear parabolic systems on a domain which is bounded in space
  and unbounded in time (namely the entire real line). We use nonlinear
  iteration arguments combined with some a priori estimates to derive
  the existence results.  We also provide conditions under which we have
  a positive solution. Some examples are given to illustrate the results.

Published February 10, 2014.
Math Subject Classifications: 35K55, 35K60.
Key Words: Nonlinear parabolic systems; nonlinear boundary conditions; 
           Caratheodory functions;  quasimonotone properties; 
           sub and supersolutions.