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Insensitizing controls for a semilinear heat equation. (English) Zbl 0942.35028

The author considers the system \[ v_t-\Delta v+f(v)=\xi +h 1_\omega\quad \text{in} Q=\Omega\times (0,T), \qquad v=0\quad \text{on} \partial\Omega\times(0,T), \]
\[ v(x,0)=y^0(x)+\tau v^0\quad \text{in} \Omega, \] where \(1_\omega\) denotes the characteristic function of \(\omega\subset \Omega;\) \(\xi, y^0\in L^2(Q)\) and \(h=h(x,t)\) is a control term in \(L^2(Q).\) \(\Phi\) is the differentiable functional \[ \Phi(v)={1\over 2}\int_{0}^{T}\int_{\mathcal O} v^2(x,t) dx dt,\qquad {\mathcal O}\subset \Omega. \] It is proved, under suitable assumptions, the existence of \(h\in L^2(Q)\) insensitizing the functional \(\Phi.\)

MSC:

35B37 PDE in connection with control problems (MSC2000)
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations

Keywords:

insensitivity
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References:

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