Null controllability of degenerate/singular parabolic equations

Abstract

The purpose of this paper is to provide a full analysis of the null controllability problem for the one dimensional degenerate/singular parabolic equation $ {u_t} - {\left( {a(x){u_x}} \right)_x} - \frac{\lambda }{{{x^\beta }}}u = 0 $ , (t, x) ? (0, T) × (0, 1), where the diffusion coefficient a(?) is degenerate at x = 0. Also the boundary conditions are considered to be Dirichlet or Neumann type related to the degeneracy rate of a(?). Under some conditions on the function a(?) and parameters β, ?, we prove global Carleman estimates. The proof is based on an improved Hardy-type inequality.