In this paper the recently introduced backstepping method for boundary control of linear partial differential equations (PDEs) is extended to plants with non-constant diffusivity/thermal conductivity and time-varying coefficients. The boundary stabilization problem is converted to a problem of solving a specific Klein-Gordon-type linear hyperbolic PDE. This PDE is then solved for a family of system parameters resulting in closed-form boundary controllers. The results of a numerical simulation are presented for the case when an explicit solution is not available. (c) 2005 Elsevier Ltd. All rights reserved.