Periodic Solutions of Evolution <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>m</mml:mi></mml:math>-Laplacian Equations with a Nonlinear Convection Term

Liu, Wenjun

doi:https://doi.org/10.1155/2007/27368

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 027368 | https://doi.org/10.1155/2007/27368

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

Wenjun Liu^1,2

Academic Editor: Vladimir Mityushev

Received24 Apr 2006

Revised23 Oct 2006

Accepted29 Nov 2006

Published03 Jan 2007

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.

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Copyright © 2007 Hindawi Publishing Corporation. 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.

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