International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 27368, 10 pages
doi:10.1155/2007/27368

Periodic Solutions of Evolution m-Laplacian Equations with a Nonlinear Convection Term

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.