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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 535629, 8 pages
http://dx.doi.org/10.1155/2013/535629
Research Article

The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation

1School of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China
2Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Received 26 March 2013; Accepted 11 June 2013

Academic Editor: Sergey Piskarev

Copyright © 2013 Juan Wang et al. 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 consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge-Ampère type. We show that such solution exists for all times and is unique. It converges eventually to a solution that satisfies a Neumann type problem for nonlinear elliptic equation of Monge-Ampère type.