SIAM Journal on Control and Optimization · 1978 · 28 citations · 14 references
Natural SciencesMathematicsPhysicsFluid DynamicsHeat TransferThermodynamicsBoundary ConditionsBoundary-value ProblemsControl TheoryOptimal ControlPartial Differential EquationsVariational FormulationHeat Diffusion EquationHyperbolic Boundary-value ProblemsHyperbolic Partial Differential EquationsOptimal Control FormulationParabolic Boundary-value ProblemsParabolic Partial Differential EquationsPartial Differential Equation Control Theory
It is verified that Russell’s results [19], [20] on exact boundary control of the wave and heat equations ($\ddot u = \Delta \dot u$, $\dot u = \Delta u$, respectively) can be extended to a class of second order hyperbolic and parabolic equations with spatially variable coefficients. For the diffusion processes a characterization is given of the ‘optimal control manifold’ $\mathfrak{M} \subset L_2 ([0,T] \times \partial \mathcal{R})$ and a continuity result is obtained for the dependence of the optimal exact control on the coefficients of the equation and the boundary operator.
14