Carleman estimates for the, one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem

[摘要] We study the observability and some of its consequences (controllability, identification of diffusion coefficients) for one-dimensional heat equations with discontinuous coefficients (piecewise C-1). The observability, for a linear equation, is obtained by a Carleman-type estimate. This kind of observability inequality yields controllability results for a semi-linear equation as well as a stability result for the identification of the diffusion coefficient. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] carleman estimate;observability;non-smooth coefficients;parabolic equations;control