Gianluca Mola – The inverse problem of recovering the reaction and the diffusion coefficients in linear parabolic equations

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Date/heure
Date(s) - 05/02/2013
10 h 00 min - 11 h 00 min

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We consider the inverse problem consisting in the identification, along with the “solution” u, of one, or both of the coefficients ? > 0 (diffusion) and ? ? R (reaction), that fulfill the parabolic equation ?tu???u=?u in ?×(0,T) for some time-instant T > 0, with initial condition u(0) = u0. We shall discuss suitable addi- tional measurements on u in order to obtain well-posedness of such an inverse problems, and will brefly describe the techniques therein involved (see [1]-[2], in collaboration with A. Lorenzi, and [3]). Moreover, we shall focus on possible generalizations of those results, and describe recent work and future developments. References [1] A. Lorenzi and G. Mola, Identification of a real constant in linear evolution equations in Hilbert spaces, to appear on Inverse Problems and Imaging, 18 (2010), 321–355 [2] A. Lorenzi and G. Mola, Recovering the reaction and the diffusion coefficients in a linear parabolic equation, Inverse Problems, 28 (2012) [3] G. Mola, Identification of the diffusion coefficient in linear evolution equations in Hilbert spaces, Journal of Abstract Differential Equations and Applications 2 (2011), 18–28