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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 22, Pages 3539-3550
http://dx.doi.org/10.1155/IJMMS.2005.3539

Viscosity solutions of fully nonlinear functional parabolic PDE

1School of Mathematics and Statistics, Wuhan University, Hubei, Wuhan 430072, China
2School of Mathematics and Statistics, HuaZhong Normal University, Hubei, Wuhan 430079, China

Received 17 October 2004; Revised 21 October 2005

Copyright © 2005 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.

Abstract

By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.