Hausdorff moments in an inverse problem for the heat equation: Numerical experiment

with C−1 ≤ ρ ≤ C, C > 1. When n = 3 it describes the evolution of temperature u in a medium where the thermal conductivity is constant and the heat capacity is ρ. It also applies to diffusion in porous rocks, where ρ is the specific storage, if the hydraulic conductivity is constant. We consider the problem of the determination of ρ in Ω from boundary measurements. Consider the system:   ∆u(x, t) = ρ(x)∂tu(x, t) u(x, 0) = 0 u(t)|∂Ω = p|∂Ω for any t ≥ 0, (2)