International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 22, Pages 3539-3550
doi:10.1155/IJMMS.2005.3539
Viscosity solutions of fully nonlinear functional parabolic PDE
Wei-An Liu1
and Gang Lu2
1School of Mathematics and Statistics, Wuhan University, Hubei, Wuhan 430072, China
2School of Mathematics and Statistics, HuaZhong Normal University, Hubei, Wuhan 430079, China
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.