Approximate controllability of the semilinear heat equation
1995 ◽
Vol 125
(1)
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pp. 31-61
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Keyword(s):
This article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain Ω when the control acts on any open and nonempty subset of Ω or on a part of the boundary. In the case of both an internal and a boundary control, the approximate controllability in LP(Ω) for 1 ≦ p < + ∞ is proved when the nonlinearity is globally Lipschitz with a control in L∞. In the case of the interior control, we also prove approximate controllability in C0(Ω). The proof combines a variational approach to the controllability problem for linear equations and a fixed point method. We also prove that the control can be taken to be of “quasi bang-bang” form.
2004 ◽
Vol 76
(3)
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pp. 475-487
2001 ◽
Vol 108
(1)
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pp. 29-64
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1995 ◽
Vol 194
(3)
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pp. 858-882
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Keyword(s):
1998 ◽
Vol 36
(6)
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pp. 2128-2147
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2018 ◽
Vol 36
(4)
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pp. 1199-1235
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1973 ◽
Vol 12
(2)
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pp. 137-154
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1999 ◽
Vol 37
(8)
◽
pp. 1059-1090
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Keyword(s):
2020 ◽
Vol 21
(7-8)
◽
pp. 727-737