Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
Null Controllability for Degenerate Parabolic Operators
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one space dimensiona ∈ C([0, 1]) ∩ C 1 (]0, 1]) and a > 0 on ]0, 1]{u t − ( a(x)u x)x = f in Q T =]0, 1[×]0, T [u(x, 0) = u 0 (x)u 0 ∈ L 2 (0, 1) , f ∈ L 2 (Q T )Campiti, Metafune, Pallara (1998)weakly degenerate case: 1/a ∈ L 1 (0, 1)H 1 a(0, 1) ={u ∈ L 2 (0, 1) ∣ ∣∫ 1strongly degenerate case: 1/a /∈ L 1 (0, 1)H 1 a(0, 1) =0{u ∈ L 2 (0, 1) ∣ ∣}aux 2 dx < ∞ & u(0) = 0 = u(1)∫ 10}aux 2 dx < ∞ & u(1) = 0