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Null controllability of degenerate/singular parabolic equations

Fotouhi, M ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1007/s10883-012-9160-5
  3. Publisher: Springer , 2012
  4. Abstract:
  5. The purpose of this paper is to provide a full analysis of the null controllability problem for the one dimensional degenerate/singular parabolic equation ut - (a(x)ux)x - λ/x βu = 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, λ, we prove global Carleman estimates. The proof is based on an improved Hardy-type inequality
  6. Keywords:
  7. Carleman estimates ; Degenerate parabolic equations ; Improved hardy inequality ; Singular potential ; Carleman estimate ; Degenerate parabolic equation ; Hardy inequality ; Null controllability ; Singular potentials ; Diffusion ; Partial differential equations ; Controllability
  8. Source: Journal of Dynamical and Control Systems ; Volume 18, Issue 4 , 2012 , Pages 573-602 ; 10792724 (ISSN)
  9. URL: http://link.springer.com/article/10.1007/s10883-012-9160-5#/page-1