PORTUGALIAE MATHEMATICA Vol. 58, No. 1, pp. 124 (2001) 

On the Lack of NullControllability of the Heat Equation on the Half SpaceSorin Micu and Enrique ZuazuaDepartamento de Matemática Aplicada, Universidad Complutense,28040 Madrid  SPAIN Emails: sorin@sunma4.mat.ucm.es zuazua@eucmax.sim.ucm.es Abstract: We study the nullcontrollability property of the linear heat equation on the halfspace with a $L^2$ Dirichlet boundary control. We rewrite the system on the similarity variables that are a common tool when analyzing asymptotic problems. By separation of variables the multidimensional control problem is reduced to an infinite family of onedimensional controlled systems. Next, the results for this type of systems proved in [18] are used in order to show that, roughly speaking, controllable data have Fourier coefficients that grow exponentially for large frequencies. This result is in contrast with the existing ones for bounded domains that guarantee that every initial datum belonging to a Sobolev space of negative order may be driven to zero in an arbitrarily small time. Keywords: Heat equation; Similarity variables; Control; Moments. Classification (MSC2000): 35B37, 35K05. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2001 Sociedade Portuguesa de Matemática
