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Null controllability for a fourth order parabolic equation

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Abstract

In the paper, the null interior controllability for a fourth order parabolic equation is obtained. The method is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of eigenfunctions of the Laplacian.

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References

  1. King B B, Stein O, Winkler M. A fourth order parabolic equation modeling epitaxial thin film growth. J Math Anal Appl, 2003, 286: 459–490

    Article  MATH  MathSciNet  Google Scholar 

  2. Fattorni H O. Boundary control systems. SIAM J Contr, 1968, 6: 349–388

    Article  Google Scholar 

  3. Fattorini H O, Russell D L. Exact controllability theorems for linear parabolic equations in one space dimension. Arch Rational Mech Anal, 1971, 43: 272–292

    Article  MATH  MathSciNet  Google Scholar 

  4. Lions J L. Exact controllability, stabilization, and perturbations for distributed systems. SIAM Rev, 1988, 30: 1–68

    Article  MATH  MathSciNet  Google Scholar 

  5. Fursikov A V, Imanuvilov O Y. Controllability of evolution Equations. Lecture Notes Series # 34. Research Institute of Mathematics, Global Analysis Research Center, Seoul National University, 1996

  6. Fernández-Cara E, Zuazua E. The cost of approximate controllability for heat equations: the linear case. Adv Differ Equ, 2000, 5: 465–514

    MATH  Google Scholar 

  7. Imanuvilov O Y. Controllability of parabolic equations, Sbornik: Mathematics, 1995, 186(6): 879–900

    Article  MathSciNet  Google Scholar 

  8. Guo Y -J L. Null boundary controllability for a fourth order parabolic equation. Taiwanese J Math, 2002, 6(3): 421–431

    MATH  MathSciNet  Google Scholar 

  9. Guo Y -J L. Littman W. Null boundary controllability for semilinear heat equations. Appl Math Optim, 1995, 32(3): 281–316

    Article  MATH  MathSciNet  Google Scholar 

  10. Lebeau G, Robbiano L. Contróle exact de l”equation de la chaleur. Comm P D E, 1995, 20: 335–356

    Article  MATH  MathSciNet  Google Scholar 

  11. Lebeau G, Zuazua E. Null controllability of a system of linear thermoelasticity. Archive Rat Mech Anal, 1998, 141(4): 297–329

    Article  MATH  MathSciNet  Google Scholar 

  12. Wang G. L ∞-null controllability for the heat equation and its concequence for the time optimal control problem. SIAM J Contr Optim, 2008, 47(4): 1701–1720

    Article  MATH  Google Scholar 

  13. Courant R, Hilbert D. Methods of Mathematical Physics. New York: Interscience Publishers, 1953

    Google Scholar 

Download references

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Hang Yu

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  1. Hang Yu
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Correspondence to Hang Yu.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 10671040, 10831007, 10801041), the National Excellent Doctoral Dissertation of China (Grant No. 200522) and the New Century Excellent Talents in University (Grant No. 06-0359)

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Yu, H. Null controllability for a fourth order parabolic equation. Sci. China Ser. F-Inf. Sci. 52, 2127–2132 (2009). https://doi.org/10.1007/s11432-009-0203-9

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  • DOI: https://doi.org/10.1007/s11432-009-0203-9

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