On the local controllability of a class of multidimensional quasilinear parabolic equations

摘要

In this Note, we study the local null controllability and the cost estimate for a class of multidimensional quasilinear parabolic equations with homogeneous Dirichlet boundary conditions and an arbitrary located internal controller. Unlike the known result for one space dimension, we need to consider the problem in the frame of classical solutions. The key point is to improve the regularity of control function for smooth data, which is a consequence of a new observability inequality for linear parabolic equations with an explicit estimate on the observability constant in terms of the C-1-norm of the principle part coefficients. The later is based on a new global Carleman estimate for the linear parabolic equation. To cite this article: X. Liu, X. Zhang, C. R. Acad. Sci. Paris, Ser. I 347 (2009).