Optimal Control of the Principal Coefficient in a Scalar Wave Equation
Optimal Control of the Principal Coefficient in a Scalar Wave Equation
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for the coefficient-to-solution mapping for discontinuous coefficients. We additionally consider a so-called "multi-bang" penalty that …