International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 27368, 10 pages
doi:10.1155/2007/27368
Research Article
Periodic Solutions of Evolution m-Laplacian Equations with a Nonlinear Convection Term
1College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
Received 24 April 2006; Revised 23 October 2006; Accepted 29 November 2006
Academic Editor: Vladimir Mityushev
Copyright © 2007 Wenjun Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We show the existence and gradient estimates of periodic solutions
in the case of 0≤α<m+1 to the evolution m-Laplacian equations of form ut−div{|∇u|m∇u}+b(u)⋅∇u=f(t)uα+h(x,t), in Ω×ℝ1 with the Dirichlet boundary value condition.