RICCATI EQUATIONS FOR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH L//2 (0,T; L//2 ( GAMMA ))-DIRICHLET BOUNDARY TERMS.

The regulator problem for second-order (linear) hyperbolic partial differential equations defined on a bounded domain OMEGA CONTAINS R**n with boundary GAMMA is studied. The distinguishing feature of the approach is that the controls are only L//2 (0, infinity ; L//2 ( GAMMA ))--functions which act in the Dirichlet boundary condition while the corresponding solutions left bracket y, y//t right bracket are penalized in the L//2 (0, infinity ; L//2 ( OMEGA )) multiplied by L//2 (0, infinity ; H-**1 ( OMEGA ))-norm