Fernández-Cara, Enrique; Guerrero, Sergio Global Carleman estimates for solutions of parabolic systems defined by transposition and some applications to controllability. (English) Zbl 1113.35037 AMRX, Appl. Math. Res. Express 2006, No. 1, Article ID75090, 31 p. (2006). The paper is concerned with application of Carleman estimates applied to exact controllability of the linear parabolic system \[ -\varphi_t - \triangle\varphi=f-\nabla F + \displaystyle{\sum_{i,j=1}^N\partial_{ij}H_ij-G_t \;,\;in\;Q=\Omega\times [0,T]\subset \mathbb R^N\times [0,T]} \]\[ \varphi=0\;on\;\partial\Omega\;,\;\varphi(T)=\varphi^o\;in\;\Omega \] with \(f,G\in L^2(Q)\;,\;F\in L^2(Q)^N\;,\;G\in C^o([0,T];H^{-1}(\Omega))\;,\;H_{ij}\in L^2(Q)\), the derivatives being taken in the generalized sense. The same problem is then considered for the nonlinear parabolic system \[ y_t - \triangle y - \varepsilon\displaystyle{\sum_{i,j=1}^Ng_{ij}(\chi,t;y,\nabla y)\partial_{ij}y=\nu 1_{\omega} \;in\;Q} \]\[ y = 0 \;on\;\Sigma=\partial\Omega\times[0,T]\;,\;y(0)=y^o\;on\;\Omega \] with \(\omega\) some small nonempty open subset of \(\Omega\). Reviewer: Vladimir Răsvan (Craiova) Cited in 8 Documents MSC: 35B45 A priori estimates in context of PDEs 35K55 Nonlinear parabolic equations 35B37 PDE in connection with control problems (MSC2000) 35K50 Systems of parabolic equations, boundary value problems (MSC2000) 93B05 Controllability Keywords:Nonlinear parabolic equation; Carleman estimate; Controllability; exact controllability × Cite Format Result Cite Review PDF Full Text: DOI