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Volumn 10, Issue 1, 2008, Pages 87-117

Optimal design under the one-dimensional wave equation

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EID: 42349112515     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/181     Document Type: Article
Times cited : (9)

References (27)
  • 1
    • 42349103772 scopus 로고    scopus 로고
    • ALLAIRE, G. Shape Optimization by the Homogenization Method. Springer (2002). Zbl 0990.35001 MR 1859696
    • ALLAIRE, G. Shape Optimization by the Homogenization Method. Springer (2002). Zbl 0990.35001 MR 1859696
  • 2
    • 27644599007 scopus 로고    scopus 로고
    • Constrained envelope for a general class of design problems
    • Zbl 1062.49011 MR 2018097
    • ARANDA, E., & PEDREGAL, P. Constrained envelope for a general class of design problems. Disc. Cont. Dyn. Syst., Suppl. Vol., (2003), 30-41. Zbl 1062.49011 MR 2018097
    • (2003) Disc. Cont. Dyn. Syst , Issue.SUPPL. VOL , pp. 30-41
    • ARANDA, E.1    PEDREGAL, P.2
  • 3
    • 36049007445 scopus 로고    scopus 로고
    • An optimal design problem in wave propagation
    • MR 2332468
    • BELLIDO, J. C., & DONOSO, A. An optimal design problem in wave propagation. J. Optim. Theory Appl. 134 (2007), 339-352. MR 2332468
    • (2007) J. Optim. Theory Appl , vol.134 , pp. 339-352
    • BELLIDO, J.C.1    DONOSO, A.2
  • 4
    • 42349091063 scopus 로고    scopus 로고
    • BENDSØE, MP., & SIGMUND, O. Topology Optimization: Theory, Methods and Aplications. Springer, Berlin (2003). Zbl 1059.74001 MR 2008524
    • BENDSØE, MP., & SIGMUND, O. Topology Optimization: Theory, Methods and Aplications. Springer, Berlin (2003). Zbl 1059.74001 MR 2008524
  • 5
    • 0035662154 scopus 로고    scopus 로고
    • Achieving arbitrarily large decay in the damped wave equation
    • Zbl 0983.35095 MR 1825863
    • CASTRO, C., & COX, S. Achieving arbitrarily large decay in the damped wave equation. SIAM J. Control Optim. 39 (2001), 1748-1755. Zbl 0983.35095 MR 1825863
    • (2001) SIAM J. Control Optim , vol.39 , pp. 1748-1755
    • CASTRO, C.1    COX, S.2
  • 6
    • 4544294079 scopus 로고    scopus 로고
    • Control of the wave equation by time-dependent coefficient
    • Zbl 1073.35032 MR 1932956
    • CHAMBOLLE, A., & SANTOSA, F. Control of the wave equation by time-dependent coefficient. ESAIMCOCV 8 (2002) 375-392. Zbl 1073.35032 MR 1932956
    • (2002) ESAIMCOCV , vol.8 , pp. 375-392
    • CHAMBOLLE, A.1    SANTOSA, F.2
  • 7
    • 42349092499 scopus 로고    scopus 로고
    • CHERKAEV, A. Variational Methods for Structural Optimization. Springer, New York (2000). Zbl 0956.74001 MR 1763123
    • CHERKAEV, A. Variational Methods for Structural Optimization. Springer, New York (2000). Zbl 0956.74001 MR 1763123
  • 8
    • 42349096459 scopus 로고    scopus 로고
    • DACOROGNA, B. Direct Method in the Calculus of Variations. Springer (1989). Zbl 0703.49001 MR 0990890
    • DACOROGNA, B. Direct Method in the Calculus of Variations. Springer (1989). Zbl 0703.49001 MR 0990890
  • 9
    • 27644579466 scopus 로고    scopus 로고
    • Optimal design of 2-D conducting graded materials by minimizing quadratic functionals in the field
    • MR 2176301
    • DONOSO, A., & PEDREGAL, P. Optimal design of 2-D conducting graded materials by minimizing quadratic functionals in the field. Struct. Multidiscip. Optim. 30 (2005), 360-367. MR 2176301
    • (2005) Struct. Multidiscip. Optim , vol.30 , pp. 360-367
    • DONOSO, A.1    PEDREGAL, P.2
  • 10
    • 0032202097 scopus 로고    scopus 로고
    • Optimizing the rate of decay of solutions of the wave equation using genetic algorithms: A counterexample to the constant damping conjecture
    • Zbl 0999.35010 MR 1655858
    • FREITAS, P. Optimizing the rate of decay of solutions of the wave equation using genetic algorithms: a counterexample to the constant damping conjecture. SIAM J. Control Optim. 37 (1999), 376-387. Zbl 0999.35010 MR 1655858
    • (1999) SIAM J. Control Optim , vol.37 , pp. 376-387
    • FREITAS, P.1
  • 11
    • 0035520196 scopus 로고    scopus 로고
    • Optimal design problems for two-phase conducting composites with weakly discontinuous objective functionals
    • Zbl 1001.49002 MR 1867929
    • GRABOVSKY, Y. Optimal design problems for two-phase conducting composites with weakly discontinuous objective functionals. Adv. Appl. Math. 27 (2001), 683-704. Zbl 1001.49002 MR 1867929
    • (2001) Adv. Appl. Math , vol.27 , pp. 683-704
    • GRABOVSKY, Y.1
  • 12
    • 0037444965 scopus 로고    scopus 로고
    • Optimal shape and position of the actuators for the stabilization of a string
    • Zbl pre05055493 MR 2020637
    • HEBRARD, P., & HENROT, A. Optimal shape and position of the actuators for the stabilization of a string. System Control Lett. 48 (2003), 199-209. Zbl pre05055493 MR 2020637
    • (2003) System Control Lett , vol.48 , pp. 199-209
    • HEBRARD, P.1    HENROT, A.2
  • 13
    • 42349099287 scopus 로고    scopus 로고
    • LIONS, J.-L., & MAGENES, E. Non-Homogeneous Boundary Value Problems and Applications. I, Springer (1972). Zbl 0223.35039 MR 0350177
    • LIONS, J.-L., & MAGENES, E. Non-Homogeneous Boundary Value Problems and Applications. Vol. I, Springer (1972). Zbl 0223.35039 MR 0350177
  • 14
    • 3042652121 scopus 로고    scopus 로고
    • LIPTON, R., & VELO, A. P. Optimal design of gradient fields with applications to electrostatics. Nonlinear Partial Differential Equations and Their Applications, College de France Seminar, XIV, D. Cioranescu and J.-L. Lions (eds.), North-Holland (2002), 509-532. Zbl 1080.78003 MR 1936008
    • LIPTON, R., & VELO, A. P. Optimal design of gradient fields with applications to electrostatics. Nonlinear Partial Differential Equations and Their Applications, College de France Seminar, Vol. XIV, D. Cioranescu and J.-L. Lions (eds.), North-Holland (2002), 509-532. Zbl 1080.78003 MR 1936008
  • 15
    • 42349107319 scopus 로고    scopus 로고
    • LURIE, K. A. Control in the coefficients of linear hyperbolic equations via spatio-temporal components. Homogenization, V. Berdichevsky et al. (eds.), World Sci., Singapore (1999), 285-315. Zbl 1035.78021 MR 1792692
    • LURIE, K. A. Control in the coefficients of linear hyperbolic equations via spatio-temporal components. Homogenization, V. Berdichevsky et al. (eds.), World Sci., Singapore (1999), 285-315. Zbl 1035.78021 MR 1792692
  • 16
    • 0000716455 scopus 로고    scopus 로고
    • The problem of the effective parameters of a mixture of two isotropic dielectrics distributed in space-time and the conservation law of wave impedance in one-dimensional wave propagation
    • Zbl 0915.35102 MR 1640028
    • LURIE, K. A. The problem of the effective parameters of a mixture of two isotropic dielectrics distributed in space-time and the conservation law of wave impedance in one-dimensional wave propagation. Proc. R. Soc. London A 454 (1998), 1767-1779. Zbl 0915.35102 MR 1640028
    • (1998) Proc. R. Soc. London A , vol.454 , pp. 1767-1779
    • LURIE, K.A.1
  • 17
    • 2942722247 scopus 로고    scopus 로고
    • m-closure of a set of isotropic dielectrics with respect to one-dimensional wave propagation. Wave Motion 40 (2004), 95-110. Zbl pre02202502 MR 2069904
    • m-closure of a set of isotropic dielectrics with respect to one-dimensional wave propagation. Wave Motion 40 (2004), 95-110. Zbl pre02202502 MR 2069904
  • 19
    • 39849088235 scopus 로고    scopus 로고
    • A spatio-temporal design problem for a damped wave equation
    • MR 2357775
    • MAESTRE, F., MÜNCH, A., & PEDREGAL, P. A spatio-temporal design problem for a damped wave equation. SIAM J. Appl. Math. 68 (2007), 109-132. MR 2357775
    • (2007) SIAM J. Appl. Math , vol.68 , pp. 109-132
    • MAESTRE, F.1    MÜNCH, A.2    PEDREGAL, P.3
  • 20
    • 42349114717 scopus 로고    scopus 로고
    • MILTON, G. W. The Theory of Composites. Cambridge Univ. Press (2002). Zbl 0993.74002 MR 1899805
    • MILTON, G. W. The Theory of Composites. Cambridge Univ. Press (2002). Zbl 0993.74002 MR 1899805
  • 21
    • 33748797939 scopus 로고    scopus 로고
    • Optimal design of the damping set for the stabilization of the wave equation
    • Zbl 1105.49005 MR 2287890
    • MÜNCH, A., PEDREGAL, P., & PERIAGO, F. Optimal design of the damping set for the stabilization of the wave equation. J. Differential Equations 231 (2006), 331-358. Zbl 1105.49005 MR 2287890
    • (2006) J. Differential Equations , vol.231 , pp. 331-358
    • MÜNCH, A.1    PEDREGAL, P.2    PERIAGO, F.3
  • 22
    • 0007009933 scopus 로고
    • Contre-exemples pour divers problemes oil le controle intervient dans les coefficients
    • Zbl 0349.49005 MR 0438205
    • MURAT, F. Contre-exemples pour divers problemes oil le controle intervient dans les coefficients. Ann. Mat. Pura Appl. 112 (1977), 49-68. Zbl 0349.49005 MR 0438205
    • (1977) Ann. Mat. Pura Appl , vol.112 , pp. 49-68
    • MURAT, F.1
  • 23
    • 30844437297 scopus 로고    scopus 로고
    • Vector variational problems and applications to optimal design
    • Zbl 1089.49022 MR 2148849
    • PEDREGAL, P. Vector variational problems and applications to optimal design. ESAIM-COCV 15 (2005), 357-381. Zbl 1089.49022 MR 2148849
    • (2005) ESAIM-COCV , vol.15 , pp. 357-381
    • PEDREGAL, P.1
  • 24
    • 4944265251 scopus 로고    scopus 로고
    • Constrained quasiconvexification of the square of the gradient of the state in optimal design
    • Zbl 1086.49013 MR 2086039
    • PEDREGAL, P. Constrained quasiconvexification of the square of the gradient of the state in optimal design. Quart. Appl. Math. 62 (2004), 459-470. Zbl 1086.49013 MR 2086039
    • (2004) Quart. Appl. Math , vol.62 , pp. 459-470
    • PEDREGAL, P.1
  • 26
    • 39849111137 scopus 로고    scopus 로고
    • Optimal design in two-dimensional conductivity for a general cost depending on the field
    • Zbl 1104.74052 MR 2276496
    • PEDREGAL, P. Optimal design in two-dimensional conductivity for a general cost depending on the field. Arch. Ration. Mech. Anal. 182 (2006), 367-385. Zbl 1104.74052 MR 2276496
    • (2006) Arch. Ration. Mech. Anal , vol.182 , pp. 367-385
    • PEDREGAL, P.1
  • 27
    • 42349114320 scopus 로고    scopus 로고
    • TARTAR, L. Remarks on optimal design problems. Calculus of Variations, Homogenization and Continuum Mechanics, G. Buttazzo et al. (eds.), World Sci., Singapore (1994), 279-296. Zbl 0884.49015 MR 1428706
    • TARTAR, L. Remarks on optimal design problems. Calculus of Variations, Homogenization and Continuum Mechanics, G. Buttazzo et al. (eds.), World Sci., Singapore (1994), 279-296. Zbl 0884.49015 MR 1428706


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