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In this paper, we study the stability in the inverse problem of determiningthe time dependent absorption coefficient appearing in the linear Boltzmannequation, from boundary observations. We prove in dimension $n\geq 2$, that theabsorption coefficient can be uniquely determined in a precise subset of thedomain, from the albedo operator. We derive a logarithm type stability estimatein the determination of the absorption coefficient from the albedo operator, ina subset of our domain assuming that it is known outside this subset. Moreover,we prove that we can extend this result to the determination of the coefficientin a larger region, and then in the whole domain provided that we have muchmore data. We prove also an identification result for the scatteringcoefficient appearing in the linear Boltzmann equation.

An inverse problem for the Linear Boltzmann Equation with time-dependent coefficient