International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 22, Pages 3539-3550
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 Liu Wei-an and Lu Gang. 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.
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.