Cannarsa, P.; Martinez, P.; Vancostenoble, J. Carleman estimates for a class of degenerate parabolic operators. (English) Zbl 1168.35025 SIAM J. Control Optim. 47, No. 1, 1-19 (2008). The authors derived new Carleman estimates for the degenerate parabolic problem \(w_t+(x^\alpha w_x)_x=f,\;(t,x)\in (0,T)\times (0,1)\) with the boundary conditions \(w(t,1)=0\) and \(w(t,0)=0,\) if \(0\leq \alpha<1\) or \((x^\alpha w_x)(t,0)=0\) if \(1\leq \alpha<2.\) The proof is based on the choice of suitable weighted functions and Hardy-type inequalities. As a consequence, for all \(0\leq \alpha<2\) and \(\omega\subset\subset (0,1)\) the null controllability results for the heat equation \(u_t-(x^\alpha u_x)_x=h\chi_\omega\) with the same boundary conditions are achieved. Reviewer: Igor Bock (Bratislava) Cited in 124 Documents MSC: 35K65 Degenerate parabolic equations 93B05 Controllability 93B07 Observability 35B45 A priori estimates in context of PDEs 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:degenerate parabolic equation; null controllability; Carleman estimates; Hardy-type inequality PDFBibTeX XMLCite \textit{P. Cannarsa} et al., SIAM J. Control Optim. 47, No. 1, 1--19 (2008; Zbl 1168.35025) Full Text: DOI