Geodesic
Numerical studies of parameter estimation techniques for nonlinear evolution equations
Kybernetika, Tome 34 (1998) no. 6, pp. 693-712 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We briefly discuss an abstract approximation framework and a convergence theory of parameter estimation for a general class of nonautonomous nonlinear evolution equations. A detailed discussion of the above theory has been given earlier by the authors in another paper. The application of this theory together with numerical results indicating the feasibility of this general least squares approach are presented in the context of quasilinear reaction diffusion equations.
We briefly discuss an abstract approximation framework and a convergence theory of parameter estimation for a general class of nonautonomous nonlinear evolution equations. A detailed discussion of the above theory has been given earlier by the authors in another paper. The application of this theory together with numerical results indicating the feasibility of this general least squares approach are presented in the context of quasilinear reaction diffusion equations.
Classification : 34G20, 65C60, 93B30, 93E10, 93E25
Keywords: nonlinear evolution equation; parameter estimation 
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Ackleh, Azmy S.; Ferdinand, Robert R.; Reich, Simeon. Numerical studies of parameter estimation techniques for nonlinear evolution equations. Kybernetika, Tome 34 (1998) no. 6, pp. 693-712. http://geodesic.mathdoc.fr/item/KYB_1998_34_6_a7/

[1] Ackleh A. S., Fitzpatrick B. G.: Estimation of time dependent parameters in general parabolic evolution systems. J. Math. Anal. Appl. 203 (1996), 464–480 | DOI | MR | Zbl

[2] Ackleh A. S., Fitzpatrick B. G.: Estimation of discontinuous parameters in general parabolic systems. Kybernetika 32 (1996), 543–556 | MR

[3] Ackleh A. S., Reich S.: Parameter Estimation in Nonlinear Evolution Equations. Numer. Funct. Anal. Optim. 19 (1998), 933–947 | DOI | MR | Zbl

[4] Banks H. T., Kunisch K.: Estimation Techniques for Distributed Parameter Systems. Birkhäuser, Boston – Basel 1989 | MR | Zbl

[5] Banks H. T., Lo C. K., Reich S., Rosen I. G.: Numerical studies of identification in nonlinear distributed parameter systems. Internat. Ser. Numer. Math. 91 (1989), 1–20 | MR | Zbl

[6] Banks H. T., Reich S., Rosen I. G.: An approximation theory for the identification of nonlinear distributed parameter systems. SIAM J. Control Optim. 28 (1990), 552–569 | DOI | MR | Zbl

[7] Banks H. T., Reich S., Rosen I. G.: Estimation of nonlinear damping in second order distributed parameter systems. Control Theory and Advanced Technology 6 (1990), 395–415 | MR

[8] Banks H. T., Reich S., Rosen I. G.: Galerkin Approximation for inverse problems for nonautonomous nonlinear distributed systems. Appl. Math. Optim. 24 (1991), 233–256 | DOI | MR | Zbl

[9] Barbu V.: Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leyden 1976 | MR | Zbl

[10] Bear J.: Dynamics of Fluids in Porous Media. Elsevier, New York 1972 | Zbl

[11] Canuto C., Quateroni A.: Approximation results for orthogonal polynomials in Sobolev spaces. Math. Comp. 38 (1982), 67–86 | DOI | MR

[12] Fitzpatrick B. G.: Analysis and approximation for inverse problems in contaminant transport and biodegradation models. Numer. Funct. Anal. Optim. 16 (1995), 847–866 | DOI | MR | Zbl

[13] Freeze R. A., Cherry J.: Groundwater. Prentice–Hall, Englewood Cliffs, N. J. 1979

[14] Johnson C.: Numerical Solution of Partial Differential Equations by The Finite Element Method. Cambridge Univ. Press, Cambridge 1987 | MR | Zbl

[15] Kluge R., Langmach H.: On some Problems of Determination of Functional Parameters in Partial Differential Equations, In: Distributed Parameter Systems: Modeling and Identification (Lecture Notes in Control and Information Sciences 1). Springer–Verlag, Berlin 1978, pp. 298–309 | MR

[16] Pao C. V.: Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York 1992 | MR | Zbl

[17] Schultz M. H.: Spline Analysis. Prentice–Hall, Englewood Cliffs, N. J. 1973 | MR | Zbl

[18] Swartz B. K., Varga R. S.: Error bounds for spline and $L$-spline interpolation. J. Approx. Theory 6 (1972), 6–49 | DOI | MR | Zbl