Barbu, Viorel Exact null internal controllability for the heat equation on unbounded convex domains. (English) Zbl 1282.93046 ESAIM, Control Optim. Calc. Var. 20, No. 1, 222-235 (2014). Summary: The liner parabolic equation \(\tfrac{\partial y}{\partial t}-\frac12\,\Delta y+F\cdot\nabla y={\vec{1}}_{\mathcal O_0}u\) with Neumann boundary condition on a convex open domain \(\mathcal O\subset \mathbb R^{d}\) with smooth boundary is exactly null controllable on each finite interval if \(\mathcal O_{0}\) is an open subset of \(\mathcal O\) which contains a suitable neighbourhood of the recession cone of \(\overline{\mathcal O}\). Here, \(F : \mathbb R^{d}\to \mathbb R^{d}\) is a bounded, \(C^{1}\)-continuous function, and \(F=\nabla g\), where \(g\) is convex and coercive. Cited in 9 Documents MSC: 93B05 Controllability 35K20 Initial-boundary value problems for second-order parabolic equations 93C20 Control/observation systems governed by partial differential equations 47D07 Markov semigroups and applications to diffusion processes Keywords:parabolic equation; null controllability; convex set; Carleman inequality PDFBibTeX XMLCite \textit{V. Barbu}, ESAIM, Control Optim. Calc. Var. 20, No. 1, 222--235 (2014; Zbl 1282.93046) Full Text: DOI Link