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Output least squares stability for the diffusion coefficient in an elliptic equation in dimension
two is analyzed. This guarantees Lipschitz stability of the solution of the least squares
formulation with respect to perturbations in the data independently of their attainability.
The analysis shows the influence of the flow direction on the parameter to be estimated.
A scale analysis for multi-scale resolution of the unknown parameter is provided.
We work on the research of a zero of a maximal monotone
operator on a real Hilbert space. Following the recent progress made in
the context of the proximal point algorithm devoted to this problem, we
introduce simultaneously a variable metric and a kind of relaxation in the
perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to
work in the context of the variational convergence theory.
The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
The soil water movement model
governed by the initial-boundary value problem for a quasilinear
1-D parabolic equation with nonlinear coefficients is considered.
The generalized statement of the problem is formulated. The
solvability of the problem is proved in a certain class of
functional spaces. The data assimilation problem for this model is
analysed. The numerical results are presented.
Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the main ideas at the core of this approach in the simpler setting of a scalar ODE. Understanding the scalar case is fundamental since the method can be straightforwardly extended to the more challenging problem of systems of ODEs. Numerical examples illustrate the...
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