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Consider a PDE, $$\partial_t u -a \nabla u - ru (1-u) = 0$$ at a given snapshot in time. The inverse problem is to find the diffusion coefficient $a \in L^{\infty}$ from a noisy measurement $$Y = \Phi(...

I am now studying Bayesian inverse problems. In the note of Dashti and Stuart https://arxiv.org/abs/1302.6989, they mentioned that "... when considering a non-separable Banach space $B$, it is ...