Null controllability of degenerate/singular parabolic equations

M. Fotouhi; L. Salimi

doi:10.1007/s10883-012-9160-5

Null controllability of degenerate/singular parabolic equations

M. Fotouhi^*
, L. Salimi

^*Corresponding author for this work

Research output: Journal Publication › Article › peer-review

26 Citations (Scopus)

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 - (a(x)u_x)_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.

Original language	English
Pages (from-to)	573-602
Number of pages	30
Journal	Journal of Dynamical and Control Systems
Volume	18
Issue number	4
DOIs	https://doi.org/10.1007/s10883-012-9160-5
Publication status	Published - Oct 2012
Externally published	Yes

Free Keywords

Carleman estimates
Degenerate parabolic equations
Improved hardy inequality
Null controllability
Singular potential

ASJC Scopus subject areas

Control and Systems Engineering
Algebra and Number Theory
Numerical Analysis
Control and Optimization

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10.1007/s10883-012-9160-5

Cite this

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title = "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 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.",

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AU - Salimi, L.

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N2 - 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.

AB - 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.

KW - Carleman estimates

KW - Degenerate parabolic equations

KW - Improved hardy inequality

KW - Null controllability

KW - Singular potential

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DO - 10.1007/s10883-012-9160-5

M3 - Article

AN - SCOPUS:84869495992

SN - 1079-2724

VL - 18

SP - 573

EP - 602

JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

IS - 4

ER -

Null controllability of degenerate/singular parabolic equations

Abstract

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ASJC Scopus subject areas

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