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Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE

E. Grenier, V. Louvet, P. Vigneaux (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Parameter estimation in non linear mixed effects models requires a large number of evaluations of the model to study. For ordinary differential equations, the overall computation time remains reasonable. However when the model itself is complex (for instance when it is a set of partial differential equations) it may be time consuming to evaluate it for a single set of parameters. The procedures of population parametrization (for instance using SAEM algorithms) are then very long and in some cases...

Preface

Guillaume Bal, Houman Owhadi (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Property C for ODE and Applications to an Inverse Problem for a Heat Equation

A. G. Ramm (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

Let j : = - d ² / d x ² + k ² q j ( x ) , k = const > 0, j = 1,2, 0 < e s s i n f q j ( x ) e s s s u p q j ( x ) < . Suppose that (*) 0 1 p ( x ) u ( x , k ) u ( x , k ) d x = 0 for all k > 0, where p is an arbitrary fixed bounded piecewise-analytic function on [0,1], which changes sign finitely many times, and u j solves the problem j u j = 0 , 0 ≤ x ≤ 1, u j ' ( 0 , k ) = 0 , u j ( 0 , k ) = 1 . It is proved that (*) implies p = 0. This result is applied to an inverse problem for a heat equation.

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