1. Department of Mathematical Sciences , University of Cincinnati , Cincinnati, Ohio, 45221, U.S.A.;2. Department of Mathematics , University of Texas at Austin , Austin, Texas, 78712, U.S.A.
Abstract:
Optimal switching for a nonlinear evolution equation is considered. A type of approximating problems with value functions {uu00} is studied. We prove that each uu is the unique viscositY solution of corresponding Hami1ton-Jacoby system, uu convergesto the value function u of the original problem as µ goes to 0, and an optimal control is determined.