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

Wenjun Liu1,2

 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

Recommended by Vladimir Mityushev

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.