Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
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two invariance problemsProblemgiven O ⊂ R n open (∂O = Γ) to study invariance of• closed domain• open domainOOKolmogorov operator{D(L 0 ) = { ϕ ∈ C(O) ∣ ∣ ϕ ∈ H 2 loc (O) , L 0ϕ ∈ C(O) }L 0 ϕ(x) := 1 2 Tr [A(x)∇2 ϕ(x)] + 〈b(x), ∇ϕ(x)〉x ∈ Owhere A(x) = σ(x)σ ∗ (x) ≥ 0oriented{distance from Γ❅d Γdist(x, Γ) if x ∈ Od Γ (x) =Γ ❅−dist(x, Γ) if x ∈ O c ❅ O ❅