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International Journal of Control Volume 15, 1972 - Issue 3
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Original Articles

Estimation of spatially varying parameters in partial differential equations†

W. H. CHEN Department of Chemical Engineering, California Institute of Technology, Pasadena, California, 91109
&
J. H. SEINFELD Department of Chemical Engineering, California Institute of Technology, Pasadena, California, 91109
Pages 487-495 | Received 21 Apr 1971, Published online: 24 Apr 2007

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Sohail R. Reddy & George S. Dulikravich. (2019) Simultaneous determination of spatially varying thermal conductivity and specific heat using boundary temperature measurements. Inverse Problems in Science and Engineering 27:11, pages 1635-1649.
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C. H. Huang & M. N. Özişik. (1991) DIRECT INTEGRATION APPROACH FOR SIMULTANEOUSLY ESTIMATING TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY AND HEAT CAPACITY. Numerical Heat Transfer, Part A: Applications 20:1, pages 95-110.
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G. P. Flach & M. N. Özişik. (1989) INVERSE HEAT CONDUCTION PROBLEM OF SIMULTANEOUSLY ESTIMATING SPATIALLY VARYING THERMAL CONDUCTIVITY AND HEAT CAPACITY PER UNIT VOLUME. Numerical Heat Transfer, Part A: Applications 16:2, pages 249-266.
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CHRISTIAN MERCKX. (1987) Identification of a spatially varying parameter in a time-periodic parabolic system. International Journal of Control 46:2, pages 699-708.
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CARLOSS. KUBRUSLY. (1977) Distributed parameter system indentification A survey†. International Journal of Control 26:4, pages 509-535.
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Ian Knowles & Robert Wallace. (1996) A variational solution for the aquifer transmissivity problem. Inverse Problems 12:6, pages 953-963.
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W.K. Yeung & T.T. Lam. (1996) Second-order finite difference approximation for inverse determination of thermal conductivity. International Journal of Heat and Mass Transfer 39:17, pages 3685-3693.
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R. E. Ewing, M. S. Pilant, J. G. Wade & A. T. Watson. 1995. Control Problems in Industry. Control Problems in Industry 119 149 .
Wing Yeung & Tung Lam. (1994) High order numerical approximation for inverse determination of thermal conductivity. High order numerical approximation for inverse determination of thermal conductivity.
R.E. Ewing, M.S. Pilant, J.G. Wade & A.T. Watson. (1994) Estimating parameters in scientific computation - A survey of experience from oil and groundwater modeling. IEEE Computational Science and Engineering 1:3, pages 19.
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Robert Acar. (1993) Identification of the Coefficient in Elliptic Equations. SIAM Journal on Control and Optimization 31:5, pages 1221-1244.
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C.H. Huang & M.N. Özişik. (1990) A irect integrationo approach for simultaneously estimating spatially varying thermal conductivity and heat capacity. International Journal of Heat and Fluid Flow 11:3, pages 262-268.
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K.-H. Hoffmann & J. Sprekels. (1986) On the Identification of Parameters in General Variational Inequalities by Asymptotic Regularization. SIAM Journal on Mathematical Analysis 17:5, pages 1198-1217.
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A.A. Georgiev. (1985) Identification of Spatially Variable Parameters in Linear Distributed Systems via Nonparametric Kernel Methods: A Convergence Study. IFAC Proceedings Volumes 18:5, pages 775-779.
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Costas Kravaris & John H. Seinfeld. (1985) Identification of Parameters in Distributed Parameter Systems by Regularization. SIAM Journal on Control and Optimization 23:2, pages 217-241.
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Richard E. Ewing & John H. George. 1985. Distributed Parameter Systems. Distributed Parameter Systems 145 161 .
Ryoichi Takahashi & Akio Arakawa. (1984) Real time application of simultaneous estimation theory for parameters and state to one-dimensional heat conduction. Nuclear Engineering and Design 81:3, pages 437-449.
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Costas Kravaris & John Seinfeld. (1983) Identification of parameters in distributed parameter systems by regularization. Identification of parameters in distributed parameter systems by regularization.
J.H. Seinfeld & C. Kravaris. 1982. Distributed Parameter Control Systems. Distributed Parameter Control Systems 367 390 .
S. K. Goyal. 1982. Finite Elements in Water Resources. Finite Elements in Water Resources 1055 1062 .
S.G. Tzafestas & P. Stavroulakis. (1981) Partioned adaptive filtering and control of distributed systems with space-dependent unknown parameters. Mathematics and Computers in Simulation 23:2, pages 206-212.
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Yvon Jarny. (1981) Identification of spatially varying parameters for a distributed system — Application to a thermal process. Mathematics and Computers in Simulation 23:2, pages 170-179.
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Tsuyoshi Okita, Yasuhide Kobayashi & Shogo Tanaka. (2007) An identification of hyperbolic distributed parameter systems using transient response. Electrical Engineering in Japan 101:3, pages 131-138.
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Sidney Yakowitz & Lucien Duckstein. (1980) Instability in aquifer identification: Theory and case studies. Water Resources Research 16:6, pages 1045-1064.
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Bernard Henri Caussade & Guy Renard. (1977) Identification de la conductivite thermique et de la chaleur specifique dans les equations de diffusion non lineaires. International Journal of Heat and Mass Transfer 20:5, pages 555-563.
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Bruno Van den Bosch. 1977. New Trends in Systems Analysis. New Trends in Systems Analysis 61 76 .
Y. Sunahara, A. Ohsumi & M. Imamura. (1976) A method of parameter identification for linear distributed parameter systems. Automatica 12:3, pages 245-256.
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S Yakowitz & P Noren. (1976) On the identification of inhomogeneous parameters in dynamic linear partial differential equations. Journal of Mathematical Analysis and Applications 53:3, pages 521-538.
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M.P. Polis & R.E. Goodson. (1976) Parameter identification in distributed systems: A synthesizing overview. Proceedings of the IEEE 64:1, pages 45-61.
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Budhi Sagar, Sidney Yakowitz & Lucien Duckstein. (1975) A direct method for the identification of the parameters of dynamic nonhomogeneous aquifers. Water Resources Research 11:4, pages 563-570.
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Raymond E. Goodson & Michael p. Polis. (1975) A Survey of Parameter Identification in Distributed Systems. IFAC Proceedings Volumes 8:1, pages 50-61.
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G. Chavent & P. Lemonnier. (1974) Identification de la Non-Linearit� D'Une �quation Parabolique Quasilineaire. Applied Mathematics and Optimization 1:2, pages 121-162.
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