HIGHLIGHTS
SUMMARY
For the sake of concreteness the authors take initial data u 0 ∈ H01 on the time interval, and 1 with u ∈ H 1, 2 ([0, T ] × ) and h ∈ H 2, 4 ([0, T ] × ∂ ) in certain mixed Sobolev spaces that are described in Sect 3. Generically, the set R (T, u 0 ) 1 1 ={v ∈ C ∞ | v(x)=u(T, x) where u(t, x) solves (1.1) for some h ∈ H 2, 4 } is referred to as the reachable set. In null controllability for the heat equation on certain Lipschitz domains (including smooth domains . . .
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