de Teresa, Luz Insensitizing controls for a semilinear heat equation. (English) Zbl 0942.35028 Commun. Partial Differ. Equations 25, No. 1-2, 39-72 (2000). 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 \(\Phi.\) Reviewer: Lubomira Softova (Bari) Cited in 1 ReviewCited in 78 Documents MSC: 35B37 PDE in connection with control problems (MSC2000) 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations Keywords:insensitivity × Cite Format Result Cite Review PDF Full Text: DOI References: [1] DOI: 10.1006/jmaa.1995.1382 · Zbl 0852.35070 · doi:10.1006/jmaa.1995.1382 [2] DOI: 10.1070/SM1995v186n06ABEH000047 · Zbl 0845.35040 · doi:10.1070/SM1995v186n06ABEH000047 [3] Fabre C., Proc. Roy. Soc. Edinburgh 125 pp 31– (1995) [4] Fernández-Cara E. Zuazua E. The cost of approximate controllability for heat equations: The linear case · Zbl 1007.93034 [5] DOI: 10.1051/cocv:1997104 · Zbl 0897.93011 · doi:10.1051/cocv:1997104 [6] Fursikov A., Controllability of evolution equations (1996) · Zbl 0862.49004 [7] Ladyzenskaja O.A., Linear and quasilinear equations of parabolic type (1968) [8] DOI: 10.1080/03605309508821097 · Zbl 0819.35071 · doi:10.1080/03605309508821097 [9] Lions J.L., Adas del Congreso de Ecuaciones Diferenciales y Aplicaciones (CEDYA) pp 43– (1989) [10] Russel D. L., Studies in Appl. Math. 52 pp 189– (1973) · Zbl 0274.35041 · doi:10.1002/sapm1973523189 [11] DOI: 10.1016/0022-0396(87)90043-X · Zbl 0631.35044 · doi:10.1016/0022-0396(87)90043-X [12] DOI: 10.1051/cocv:1997106 · Zbl 0895.93023 · doi:10.1051/cocv:1997106 [13] Zuazua E., J. Maths, pures et appl 69 pp 33– (1990) [14] DOI: 10.1016/S0021-7824(97)89951-5 · Zbl 0872.93014 · doi:10.1016/S0021-7824(97)89951-5 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.