zbMATH — the first resource for mathematics

Estimation of discontinuous parameters in general nonautonomous parabolic systems. (English) Zbl 1043.65512

65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
Full Text: Link EuDML
[1] A. S. Ackleh, B. G. Fitzpatrick: Estimation of time dependent parameters in general parabolic evolution systems. J. Math. Anal. Appl. 203 (1996), 464-480. · Zbl 0869.35047 · doi:10.1006/jmaa.1996.0391
[2] A. S. Ackleh, B. G. Fitzpatrick: Estimation of temporally discontinuous parameters in general parabolic evolution systems. Proceedings of the 3rd IEEE Mediterranean Symposium on New Directions in Control and Automation, vol. 1, pp. 280-286.
[3] H. T. Banks: Computational techniques for inverse problems in size structured stochastic population models. Control of Partial Differential Equations (A. Bermudez, (Lecture Notes in Control and Inform. Sci. 114), Springer-verlag, Berlin 1989, pp. 3-10. · Zbl 0716.93062
[4] H. T. Banks L. W. Botsford F. Kappel, C. Wang: Modeling and estimation in size structured population models. Mathematical Ecology, Proceeding of the Autumn Course Research Seminars (T. G. Hallam, L.J. Gross and S. A. Levin, World Scientific, 1988, pp. 521-541.
[5] H. T. Banks, J. M. Crowley: Parameter Estimation for Distributed Systems Arising in Elasticity. LCDS Report No. 81–24, Brown University. Proc. Symposium on Engineering Sciences and Mechanics, National Cheng Kung University, Tainan 1981, pp. 158-177.
[6] H. T. Banks J. M. Crowley, I. G. Rosen: Methods for the identification of material parameters in distributed models for flexible structures. Mat. Apl. Comput. 5 (1986), 2, 139-168. · Zbl 0631.93017
[7] H. T. Banks, K. Ito: A unified framework for approximation in inverse problems for distributed parameter systems. Control Theory Advanced Technology 4 (1988), 1, 73-90.
[8] H. T. Banks, K. Kunisch: Estimation Techniques for Distributed Parameter Systems. Birkhäuser, Boston–Basel 1989. · Zbl 0695.93020
[9] V. Barbu: Convexity and optimization in Banach spaces. Editura Academiei, Holland 1986. · Zbl 0594.49001
[10] C. Canuto, A. Quateroni: Approximation results for orthogonal polynomials in Sobolev spaces. Math. Comp. 38 (1982), 157, 67-86. · Zbl 0567.41008 · doi:10.2307/2007465
[11] O. Diekmann M. Gyllenberg, H. R. Thieme: Perturbing evolutionary systems by step responses and cumulative outputs. Differential Integral Equations 8 (1995), 1205-1244. · Zbl 0834.47043
[12] N. Dunford, T. Schwartz: Linear Operators Part I: General Theory. Interscience Publishers, New York 1958. · Zbl 0084.10402
[13] E. Giusti: Minimal Surfaces and Functions of Bounded Variations. Birkhäuser, Boston–Basel 1976.
[14] S. Gutman: Identification of discontinuous parameters in flow equations. SIAM J. Control Optim. 28 (1990), 1049-1060. · Zbl 0734.35152 · doi:10.1137/0328057
[15] C. Johnson: Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge Press, Cambridge 1987. · Zbl 0628.65098
[16] P. K. Lamm: Estimation of discontinuous coefficients in parabolic systems: Applications to reservoir simulation. SIAM J. Control Optim. 25 (1987), 18-37. · Zbl 0612.93014 · doi:10.1137/0325002
[17] P. K. Lamm, K. A. Murphy: Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems. Quart. Appl. Math. 46 (1988), 1-22. · Zbl 0645.65087
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.