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Open Access Research

Uniform attractors for the non-autonomous p-Laplacian equations with dynamic flux boundary conditions

Kun Li1 and Bo You2*

Author Affiliations

1 Department of Basic, Henan Mechanical and Electrical Engineering College, Xinxiang, 453003, P.R. China

2 School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

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Boundary Value Problems 2013, 2013:128  doi:10.1186/1687-2770-2013-128

Published: 17 May 2013

Abstract

This paper studies the long-time asymptotic behavior of solutions for the non-autonomous p-Laplacian equations with dynamic flux boundary conditions in n-dimensional bounded smooth domains. We have proved the existence of the uniform attractor in <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/128/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/128/mathml/M1">View MathML</a> for the non-autonomous p-Laplacian evolution equations subject to dynamic nonlinear boundary conditions by using the Sobolev compactness embedding theory, and the existence of the uniform attractor in <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/128/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/128/mathml/M2">View MathML</a> by asymptotic a priori estimate.