메뉴 건너뛰기




Volumn 7, Issue 1, 2013, Pages 159-182

Inverse problem for a coupled parabolic system with discontinuous conductivities: One-dimensional case

Author keywords

Carleman; Interior point method; Inverse problems; Parabolic system; Quadratic programming

Indexed keywords


EID: 84874257919     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2013.7.159     Document Type: Article
Times cited : (12)

References (30)
  • 1
    • 80052681864 scopus 로고    scopus 로고
    • Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems
    • INRIA
    • F. Alvarez, J. Bolte, J. F. Bonnans and F. Silva, Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems, Technical Report RR 6863, INRIA, (2009).
    • (2009) Technical Report RR 6863
    • Alvarez, F.1    Bolte, J.2    Bonnans, J.F.3    Silva, F.4
  • 2
    • 70449670812 scopus 로고    scopus 로고
    • Inverse problem for a parabolic system with two components by measurements of one component
    • A. Benabdallah, M. Cristofol, P. Gaitan and M. Yamamoto, Inverse problem for a parabolic system with two components by measurements of one component, Applicable Analysis, 88 (2008), 683-709.
    • (2008) Applicable Analysis , vol.88 , pp. 683-709
    • Benabdallah, A.1    Cristofol, M.2    Gaitan, P.3    Yamamoto, M.4
  • 3
    • 74449089947 scopus 로고    scopus 로고
    • A new Carleman inequality for parabolic systems with a single observation and applications
    • A. Benabdallah, M. Cristofol, P. Gaitan and L. de Teresa, A new Carleman inequality for parabolic systems with a single observation and applications, C. R. Math. Acad. Sci. Paris, 348 (2010), 25-29.
    • (2010) C. R. Math. Acad. Sci. Paris , vol.348 , pp. 25-29
    • Benabdallah, A.1    Cristofol, M.2    Gaitan, P.3    de Teresa, L.4
  • 4
    • 34548171032 scopus 로고    scopus 로고
    • Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and a inverse problem
    • A. Benabdallah, Y. Dermenjian and J. Le Rousseau, Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and a inverse problem, Journal of Mathematical Analysis and Applications, 336 (2007), 865-887.
    • (2007) Journal of Mathematical Analysis and Applications , vol.336 , pp. 865-887
    • Benabdallah, A.1    Dermenjian, Y.2    Le Rousseau, J.3
  • 5
    • 52649171353 scopus 로고    scopus 로고
    • Stability of discontinuous diffusion coefficients and initial conditions in an inverse problem for the heat equation
    • A. Benabdallah, P. Gaitan and J. Le Rousseau, Stability of discontinuous diffusion coefficients and initial conditions in an inverse problem for the heat equation, SIAM Journal on Control and Optimization, 46 (2007), 1849-1881.
    • (2007) SIAM Journal On Control and Optimization , vol.46 , pp. 1849-1881
    • Benabdallah, A.1    Gaitan, P.2    Le Rousseau, J.3
  • 8
    • 84874229591 scopus 로고    scopus 로고
    • Identification of two coefficients with data of one component for a nonlinear parabolic system
    • M. Cristofol, P. Gaitan, H. Ramoul and M. Yamamoto, Identification of two coefficients with data of one component for a nonlinear parabolic system, Applicable Analysis, (2011), 1-9.
    • (2011) Applicable Analysis , pp. 1-9
    • Cristofol, M.1    Gaitan, P.2    Ramoul, H.3    Yamamoto, M.4
  • 10
    • 79955977339 scopus 로고    scopus 로고
    • Discretization of interior point methods for state constrained elliptic optimal control problems: Optimal error estimates and parameter adjustment
    • M. Hinze and A. Schiela, Discretization of interior point methods for state constrained elliptic optimal control problems: Optimal error estimates and parameter adjustment, Computational Optimization and Applications, 48 (2010), 581-600.
    • (2010) Computational Optimization and Applications , vol.48 , pp. 581-600
    • Hinze, M.1    Schiela, A.2
  • 13
    • 79951853718 scopus 로고    scopus 로고
    • Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces
    • J. Le Rousseau and L. Robbiano, Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces, Inventiones Mathematicae, 183 (2011), 245-336.
    • (2011) Inventiones Mathematicae , vol.183 , pp. 245-336
    • Le Rousseau, J.1    Robbiano, L.2
  • 15
    • 0000561116 scopus 로고
    • On the implementation of a primal-dual interior point method
    • S. Mehrotra, On the implementation of a primal-dual interior point method, SIAM Journal on Optimization, 2 (1992), 575-601.
    • (1992) SIAM Journal On Optimization , vol.2 , pp. 575-601
    • Mehrotra, S.1
  • 16
    • 67349108243 scopus 로고    scopus 로고
    • Strategies for time-dependent PDE control using an integrated modeling and simulation environment. Part one: Problems without inequality constraints
    • Matheon, Berlin
    • I. Neitzel, U. Prüfert and T. Slawig, Strategies for time-dependent PDE control using an integrated modeling and simulation environment. Part one: problems without inequality constraints, Technical Report 408, Matheon, Berlin, (2007).
    • (2007) Technical Report , vol.408
    • Neitzel, I.1    Prüfert, U.2    Slawig, T.3
  • 17
    • 67349135759 scopus 로고    scopus 로고
    • Strategies for time-dependent PDE control with inequality constraints using an integrated modeling and simulation environment
    • I. Neitzel, U. Prüfert and T. Slawig, Strategies for time-dependent PDE control with inequality constraints using an integrated modeling and simulation environment, Numerical Algorithms, 50 (2008), 241-269.
    • (2008) Numerical Algorithms , vol.50 , pp. 241-269
    • Neitzel, I.1    Prüfert, U.2    Slawig, T.3
  • 19
    • 42549154196 scopus 로고    scopus 로고
    • Uniqueness and Ḧolder stability of discontinuous diffusion coefficients in three related inverse problems for the heat equation
    • O. Poisson, Uniqueness and Ḧolder stability of discontinuous diffusion coefficients in three related inverse problems for the heat equation, Inverse Problems, 24 (2008), 025012, 32 pp.
    • (2008) Inverse Problems , vol.24 , pp. 32
    • Poisson, O.1
  • 20
    • 34848876059 scopus 로고    scopus 로고
    • An interior point method for a parabolic optimal control problem with regularized pointwise state constraints
    • U. Prüfert and F. Tröltzsch, An interior point method for a parabolic optimal control problem with regularized pointwise state constraints, ZAMM Z. Angew. Math. Mech., 87 (2007), 564-589.
    • (2007) ZAMM Z. Angew. Math. Mech , vol.87 , pp. 564-589
    • Prüfert, U.1    Tröltzsch, F.2
  • 21
    • 84863838364 scopus 로고    scopus 로고
    • The inverse problem of determining several coefficients in a non linear Lotka-Volterra system
    • L. Roques and M. Cristofol, The inverse problem of determining several coefficients in a non linear Lotka-Volterra system, Inverse Problems, 28 (2012), 075007, 12 pp.
    • (2012) Inverse Problems , vol.28 , pp. 12
    • Roques, L.1    Cristofol, M.2
  • 22
    • 77955569885 scopus 로고    scopus 로고
    • Erratum to: Stability of diffusion coefficients in an inverse problem for the lotka-volterra competition system
    • K. Sakthivel, N. Branibalan, J.-H. Kim and K. Balachandran, Erratum to: Stability of diffusion coefficients in an inverse problem for the lotka-volterra competition system, Acta Applicandae Mathematicae, 111 (2010), 149-152.
    • (2010) Acta Applicandae Mathematicae , vol.111 , pp. 149-152
    • Sakthivel, K.1    Branibalan, N.2    Kim, J.-H.3    Balachandran, K.4
  • 23
    • 70450176564 scopus 로고    scopus 로고
    • Barrier methods for optimal control problems with state constraints
    • A. Schiela, Barrier methods for optimal control problems with state constraints, SIAM Journal on Optimization, 20 (2009), 1002-1031.
    • (2009) SIAM Journal On Optimization , vol.20 , pp. 1002-1031
    • Schiela, A.1
  • 24
    • 80052672428 scopus 로고    scopus 로고
    • An interior point algorithm with inexact step computation in function space for state constrained optimal control
    • A. Schiela and A. Günther, An interior point algorithm with inexact step computation in function space for state constrained optimal control, Numerische Mathematik, 119 (2011), 373-407.
    • (2011) Numerische Mathematik , vol.119 , pp. 373-407
    • Schiela, A.1    Günther, A.2
  • 25
    • 49149108125 scopus 로고    scopus 로고
    • Superlinear convergence of the control reduced interior point method for PDE constrained optimization
    • A. Schiela and M. Weiser, Superlinear convergence of the control reduced interior point method for PDE constrained optimization, Computational Optimization and Applications, 39 (2008), 369-393.
    • (2008) Computational Optimization and Applications , vol.39 , pp. 369-393
    • Schiela, A.1    Weiser, M.2
  • 26
    • 46749103269 scopus 로고    scopus 로고
    • Primal-dual interior point methods for PDE-constrained optimization
    • M. Ulbrich and S. Ulbrich, Primal-dual interior point methods for PDE-constrained optimization, Mathematical Programming, 117 (2009), 435-485.
    • (2009) Mathematical Programming , vol.117 , pp. 435-485
    • Ulbrich, M.1    Ulbrich, S.2
  • 28
    • 48349146050 scopus 로고    scopus 로고
    • Control reduced primal interior point method for a class of control constrained optimal control problems
    • M. Weiser, T. Gänzler and A. Schiela, A control reduced primal interior point method for a class of control constrained optimal control problems, Computational Optimization and Applications, 41 (2008), 127-145.
    • (2008) Computational Optimization and Applications , vol.41 , pp. 127-145
    • Weiser, M.1    Gänzler, T.2    Schiela, A.3
  • 30
    • 77956779125 scopus 로고    scopus 로고
    • A posteriori error estimates for a finite element discretization of interior point methods for an elliptic optimization problem with state constraints
    • W. Wollner, A posteriori error estimates for a finite element discretization of interior point methods for an elliptic optimization problem with state constraints, Computational Optimization and Applications, 47 (2010), 133-159.
    • (2010) Computational Optimization and Applications , vol.47 , pp. 133-159
    • Wollner, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.