Regularity of pointwise boundary control systems (Q1198673)

The generalized heat and wave equations \[ \partial_ t u+Au=0,\qquad \partial_ t^ 2 u+Au=0, \qquad 0<t<T \] are considered, with boundary control given by \(\gamma u=\) trace of \(u\) on boundary \(=\delta_{a'}f(x)\) and it is shown that \(u(t)\not\in L^ 2(\Omega)\) is general. By imposing regularity conditions on \(f\) on the form \(f=\{f_ j\}\), \(f_ j\in C_ 0^ k([0,T])\) it is shown that the solutions are continuous from \([0,T]\) into \(L^ 2(\Omega)\).