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Two problems arising in Environment are considered. The first one concerns a conjecture posed by von Neumann in 1955 on the possible modification of the albedo in order to control the Earth surface temperature. The second one is related to the approximate controllability of Stackelberg-Nash strategies for some optimization problems as, for instance, the pollution control in a lake. The results of the second part were obtained in collaboration with Jacques-Lois Lions.
FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model...
We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction (cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously known (single...
We recently derived a very general representation formula
for the boundary voltage perturbations caused by internal
conductivity inhomogeneities of low volume fraction (
cf. Capdeboscq and Vogelius (2003)). In this paper we show how this
representation formula may be used to obtain very
accurate estimates for the size of the inhomogeneities
in terms of multiple boundary measurements. As demonstrated
by our computational experiments, these estimates are significantly
better than previously known...
The paper presents some results related to
the optimal control approachs applying to inverse radiative transfer
problems, to the theory of reflection operators, to the solvability of the
inverse problems on boundary function and to algorithms for solution of
these problems.
We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves...
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