Numerical approximation for a time optimal control problems governed by semi-linear heat equations

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• 作者：Guojie Zheng (4) (5)
  Jingben Yin (6)
  
  4. College of Mathematics and Information Science ; Henan Normal University ; Xinxiang ; 453007 ; P.R. China
  5. School of Computational and Applied Mathematics ; University of the Witwatersrand ; Wits ; 2050 ; Johannesburg ; South Africa
  6. Department of Mathematics ; Henan Institute of Science and Technology ; Xinxiang ; 453003 ; P.R. China
  
• 关键词：heat equation ; time optimal control ; finite element methods ; numerical approximation
• 刊名：Advances in Difference Equations
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：225 KB
• 参考文献：1. Cazenave, T, Haraux, A (1998) An Introduction to Semilinear Evolution Equations. Clarendon, Oxford
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  5. Wang, G, Zheng, G (2012) An approach to the optimal time for a time optimal control problem of an internally controlled heat equation. SIAM J. Control Optim 50: pp. 601-628 CrossRef
  6. Ciarlet, P (1978) The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam
  7. Chrysafinos, K, Hou, LS (2002) Error estimates for semidiscrete finite element approximations of linear and semilinear parabolic equations under minimal regularity assumptions. SIAM J. Numer. Anal 40: pp. 282-306 CrossRef
  8. Thom茅e, V (1997) Galerkin Finite Element Methods for Parabolic Equations. Springer, Berlin CrossRef
  9. Barbu, V (1993) Analysis and Control of Nonlinear Infinite Dimensional Systems. Academic Press, New York
  10. Li, X, Yong, J (1995) Optimal Control Theory for Infinite Dimensional Systems. Birkh盲user Boston, Cambridge CrossRef
  11. Wang, G (2008) -Null controllability for the heat equation and its consequences for the time optimal control problem. SIAM J. Control Optim 47: pp. 1701-1720 CrossRef
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this paper, we study the optimal time for a time optimal control problem , governed by an internally controlled semi-linear heat equation. By projecting the original problem via the finite element method, we obtain another time optimal control problem governed by a semi-linear system of ordinary differential equations. Here, h is the mesh sizes of the finite element spaces. The purpose of this study is to approach the optimal time for the problem through the optimal time for the problem . We obtain error estimates between the optimal times in terms of h. MSC: 35K05, 49J20.