In this paper, the spatial behavior of solutions of a class of nonlinear parabolic equations is studied. We obtain some alternative results for the solutions under suitable conditions on the nonlinear terms. The main tool used is the weighted energy method. Our results can be viewed as a version of Saint-Venant's principle to the parabolic equations. © 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Liu, Y., Du, Y., & Yao, Z. (2010). Some alternative results for some nonlinear parabolic equations in the half cylinder. Journal of the Franklin Institute, 347(8), 1475–1488. https://doi.org/10.1016/j.jfranklin.2010.07.001