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**On the identification of coefficients of elliptic problems by asymptotic regularization.**
*(English)*
Zbl 0576.65121

The problem of the identification of functional coefficients of elliptic boundary value problems from measured data is considered. A new and interesting method is developed to identify the unknown coefficients without minimization techniques. The original problem is embedded in a family of parabolic evolution equations and the required coefficients matrix is found out to be the weak \(L^ 2\)-limit for \(t\to \infty\). Finite dimensional Galerkin approximations are introduced in order to obtain a computational technique and a similar asymptotic behavior is proved for them. A stability result is also given for the Galerkin approximations.

Reviewer: V.Arnăutu (Iaşi)

### MSC:

65Z05 | Applications to the sciences |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

35R30 | Inverse problems for PDEs |

35J25 | Boundary value problems for second-order elliptic equations |

### Keywords:

identification of coefficients; asymptotic regularization; measured; data; Galerkin approximations; asymptotic behavior; stability### References:

[1] | Alt H. W., Ser. Numer. Math. |

[2] | Chavent G., Third IFAC Symposium, The Hague/Delft (1973) |

[3] | Hoffmann K.-H., Towards the identification of ordinary differential equations from measurements · Zbl 0665.34013 |

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