Stability of the determination of a time-dependent coefficient in parabolic equations
نویسندگان
چکیده
We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coe cient σ(t), appearing in a Dirichlet initial-boundary value problem for the parabolic equation ∂tu − ∆xu + σ(t)f(x)u = 0, from Neumann boundary data. We extend this result to the same inverse problem when the previous linear parabolic equation is changed to the semi-linear parabolic equation ∂tu− ∆xu = F (t, x, σ(t), u(x, t)).
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