메뉴 건너뛰기




Volumn 70, Issue 6, 2009, Pages 2366-2375

Optimal control of a nonlinear parabolic-elliptic system

Author keywords

Distributed optimal control; Optimal control; Optimal solution; The parabolic elliptic system

Indexed keywords

CONTROL THEORY; INTERSECTIONS; OPTIMAL CONTROL SYSTEMS; OPTIMAL SYSTEMS; OPTIMIZATION; PROGRAMMING THEORY; SYSTEM THEORY; SYSTEMS ENGINEERING;

EID: 59049090852     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2008.03.018     Document Type: Article
Times cited : (3)

References (34)
  • 2
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • Camassa R., and Holm D.D. An integrable shallow water equation with peaked solitons. Physical Review Letters 71 11 (1993) 1661-1664
    • (1993) Physical Review Letters , vol.71 , Issue.11 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 3
    • 0037171407 scopus 로고    scopus 로고
    • Camassa-Holm, Korteweg-de Vries and related models for water waves
    • Johnson R.S. Camassa-Holm, Korteweg-de Vries and related models for water waves. Journal of Fluid Mechanics 455 (2002) 63-82
    • (2002) Journal of Fluid Mechanics , vol.455 , pp. 63-82
    • Johnson, R.S.1
  • 4
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic flow on the diffeomorphism group of the circle
    • Constantin A., and Kolev B. Geodesic flow on the diffeomorphism group of the circle. Commentarii Mathematici Helvetici 78 (2003) 787-804
    • (2003) Commentarii Mathematici Helvetici , vol.78 , pp. 787-804
    • Constantin, A.1    Kolev, B.2
  • 5
    • 0034415062 scopus 로고    scopus 로고
    • Existence of permanent and breaking waves for a shallow water equation: A geometric approach
    • Constantin A. Existence of permanent and breaking waves for a shallow water equation: A geometric approach. Annals de I'Institut Fourier 50 (2000) 321-362
    • (2000) Annals de I'Institut Fourier , vol.50 , pp. 321-362
    • Constantin, A.1
  • 6
    • 0034729052 scopus 로고    scopus 로고
    • Stability of a class of solitary waves in compressible elastic rods
    • Constantin A., and Strauss W. Stability of a class of solitary waves in compressible elastic rods. Physics Letters A 270 (2000) 140-148
    • (2000) Physics Letters A , vol.270 , pp. 140-148
    • Constantin, A.1    Strauss, W.2
  • 7
    • 0031679566 scopus 로고    scopus 로고
    • Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
    • Dai H.H. Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod. Acta Mechanica 127 (1998) 193-207
    • (1998) Acta Mechanica , vol.127 , pp. 193-207
    • Dai, H.H.1
  • 9
    • 0032374820 scopus 로고    scopus 로고
    • Well-posedness, global existence and blowup phenomena for a periodic quasi-linear hyperbolic equation
    • Constantin A., and Escher J. Well-posedness, global existence and blowup phenomena for a periodic quasi-linear hyperbolic equation. Communications Pure Applied Mathematics 51 (1998) 475-504
    • (1998) Communications Pure Applied Mathematics , vol.51 , pp. 475-504
    • Constantin, A.1    Escher, J.2
  • 12
    • 0034394008 scopus 로고    scopus 로고
    • On the weak solutions to a shallow water equation
    • Xin Z., and Zhang P. On the weak solutions to a shallow water equation. Communications Pure Applied Mathematics 11 (2000) 1411-1433
    • (2000) Communications Pure Applied Mathematics , vol.11 , pp. 1411-1433
    • Xin, Z.1    Zhang, P.2
  • 13
    • 18244365592 scopus 로고    scopus 로고
    • A blow-up result for the periodic Camassa-Holm equation
    • Wahlen E. A blow-up result for the periodic Camassa-Holm equation. Archiv der Mathematik 84 (2005) 334-340
    • (2005) Archiv der Mathematik , vol.84 , pp. 334-340
    • Wahlen, E.1
  • 14
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • Constantin A., and Escher J. Wave breaking for nonlinear nonlocal shallow water equations. Acta Mathematica 181 (1998) 229-243
    • (1998) Acta Mathematica , vol.181 , pp. 229-243
    • Constantin, A.1    Escher, J.2
  • 15
    • 0043159153 scopus 로고    scopus 로고
    • A note on well-posedness for Camassa-Holm equation
    • Danchin. A note on well-posedness for Camassa-Holm equation. Journal of Differential Equations 192 2 (2003) 429-444
    • (2003) Journal of Differential Equations , vol.192 , Issue.2 , pp. 429-444
    • Danchin1
  • 16
    • 0037281017 scopus 로고    scopus 로고
    • On the Cauchy problem for a nonlinearly dispersive wave equation
    • Yin Z. On the Cauchy problem for a nonlinearly dispersive wave equation. Journal of Nonlinear Mathematical Physics 10 1 (2003) 10-15
    • (2003) Journal of Nonlinear Mathematical Physics , vol.10 , Issue.1 , pp. 10-15
    • Yin, Z.1
  • 18
    • 0004159331 scopus 로고    scopus 로고
    • A reduced-basis method for control problems governed by PDES. Control and estimation of distributed parameter systems
    • Ito K., and Ravindran S.S. A reduced-basis method for control problems governed by PDES. Control and estimation of distributed parameter systems. International Series of Numerical Mathematics 126 (1998) 153-168
    • (1998) International Series of Numerical Mathematics , vol.126 , pp. 153-168
    • Ito, K.1    Ravindran, S.S.2
  • 19
    • 0035191261 scopus 로고    scopus 로고
    • Proper orthogonal decomposition for reduced basis feedback controller for parabolic equation
    • Atweil J.A., and King B.B. Proper orthogonal decomposition for reduced basis feedback controller for parabolic equation. Mathematical and Modelling 33 (2001) 1-19
    • (2001) Mathematical and Modelling , vol.33 , pp. 1-19
    • Atweil, J.A.1    King, B.B.2
  • 21
    • 59049097709 scopus 로고    scopus 로고
    • S. Volkwein, Mesh-independence of an augmented Lagrangian-SQP method in Hilbert spaces and control problems for Burgers equation, Ph.D. Thesis, Department of mathematics, Technical University of Berlin, October, 1997
    • S. Volkwein, Mesh-independence of an augmented Lagrangian-SQP method in Hilbert spaces and control problems for Burgers equation, Ph.D. Thesis, Department of mathematics, Technical University of Berlin, October, 1997
  • 22
    • 0036643357 scopus 로고    scopus 로고
    • Analysis of instantaneous control for the Burgers equation
    • Hinze M., and Volkwein S. Analysis of instantaneous control for the Burgers equation. Nonlinear Analysis 50 1 (2002) 1-26
    • (2002) Nonlinear Analysis , vol.50 , Issue.1 , pp. 1-26
    • Hinze, M.1    Volkwein, S.2
  • 24
    • 36749074766 scopus 로고    scopus 로고
    • Optimal control of KdV-Burgers equation
    • Zhu M., Tian L., and Zhao Z. Optimal control of KdV-Burgers equation. Journal of Jiangsu University 25 3 (2004) 235-238
    • (2004) Journal of Jiangsu University , vol.25 , Issue.3 , pp. 235-238
    • Zhu, M.1    Tian, L.2    Zhao, Z.3
  • 25
    • 36749080762 scopus 로고    scopus 로고
    • Optimal control of sufficient nonlinear KdV-Burgers equation
    • Zhao Z., and Tian L. Optimal control of sufficient nonlinear KdV-Burgers equation. Journal of Jiangsu University 26 2 (2005) 140-143
    • (2005) Journal of Jiangsu University , vol.26 , Issue.2 , pp. 140-143
    • Zhao, Z.1    Tian, L.2
  • 26
    • 0001841018 scopus 로고    scopus 로고
    • Feedback control of Kuramoto-Sivashinsky equation
    • Armaou A., and Christofides P.D. Feedback control of Kuramoto-Sivashinsky equation. Physics D 137 (2000) 49-61
    • (2000) Physics D , vol.137 , pp. 49-61
    • Armaou, A.1    Christofides, P.D.2
  • 27
    • 36749104043 scopus 로고    scopus 로고
    • Optimal control of Kuramoto-Sivashinsky equation
    • Zhao Z. Optimal control of Kuramoto-Sivashinsky equation. International Journal of Nonlinear Science 1 1 (2006) 54-58
    • (2006) International Journal of Nonlinear Science , vol.1 , Issue.1 , pp. 54-58
    • Zhao, Z.1
  • 28
    • 15244351766 scopus 로고    scopus 로고
    • Optimal control of stochastic partial differential equations
    • Oksendal B. Optimal control of stochastic partial differential equations. Stochastic Analysis and Applications 23 1 (2005) 165-179
    • (2005) Stochastic Analysis and Applications , vol.23 , Issue.1 , pp. 165-179
    • Oksendal, B.1
  • 29
    • 0037445050 scopus 로고    scopus 로고
    • Time-domain decomposition of optimal control problems for the wave equation
    • Lagnese J.E., and Leugering G. Time-domain decomposition of optimal control problems for the wave equation. System and Control Letters 48 (2003) 229-242
    • (2003) System and Control Letters , vol.48 , pp. 229-242
    • Lagnese, J.E.1    Leugering, G.2
  • 30
    • 0031572072 scopus 로고    scopus 로고
    • Optimal control of two- and three-dimensional incompressible Navier-Stokes flows
    • Ghattas O., and Bark J.-H. Optimal control of two- and three-dimensional incompressible Navier-Stokes flows. Journal of Computational Physics 136 (1997) 231-244
    • (1997) Journal of Computational Physics , vol.136 , pp. 231-244
    • Ghattas, O.1    Bark, J.-H.2
  • 31
    • 0037089754 scopus 로고    scopus 로고
    • Optimal boundary control of the heat equation with target function at terminal time
    • Ji G., and Martin C. Optimal boundary control of the heat equation with target function at terminal time. Applied Mathematics and Computation 127 (2002) 335-345
    • (2002) Applied Mathematics and Computation , vol.127 , pp. 335-345
    • Ji, G.1    Martin, C.2
  • 32
    • 50349096457 scopus 로고    scopus 로고
    • Optimal control of the viscous Camassa-Holm equation
    • 10.1016/j.nonrwa.2007.10.016
    • Tian L., et al. Optimal control of the viscous Camassa-Holm equation. Nonlinear Analysis: Real World Applications (2007) 10.1016/j.nonrwa.2007.10.016
    • (2007) Nonlinear Analysis: Real World Applications
    • Tian, L.1
  • 33
    • 0003542431 scopus 로고
    • Springer-Verlag, Berlin
    • Dautray R., and Lions J.L. Mathematical Analysis and Numerical Methods for Science and Technology. Evolution Problems I vol. 5 (1992), Springer-Verlag, Berlin
    • (1992) Evolution Problems I , vol.5
    • Dautray, R.1    Lions, J.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.