Inverse time-dependent perfusion coefficient identification

Inverse space-dependent perfusion coefficient identification

The identification of the space-dependent perfusion coefficient in the onedimensional transient bio-heat conduction equation is investigated. In this inverse coefficient identification problem, the additional measurement necessary to render a unique solution is a boundary temperature measurement. A numerical approach based on a Crank-Nicolson finitedifference scheme combined with Tikhonov’s reg...

AN INVERSE PROBLEM FOR THE WAVE EQUATION WITH A TIME DEPENDENT COEFFICIENT Rakesh

Let Ω ⊂ R, n ≥ 2, be a bounded domain with smooth boundary. Consider utt −4xu+ q(x, t)u = 0 in Ω× [0, T ] u(x, 0) = 0, ut(x, 0) = 0 if x ∈ Ω u(x, t) = f(x, t) on ∂Ω× [0, T ] We show that if u and f are known on ∂Ω× [0, T ], for all f ∈ C∞ 0 (∂Ω× [0, T ]), then q(x, t) may be reconstructed on C = { (x, t) : x∈Ω, 0 < t < T, x− tω & x+ (T − t)ω 6∈ Ω ∀ ω ∈ R, |ω| = 1 } provided q is known at all po...

Regularization and Hölder Type Error Estimates for an Initial Inverse Heat Problem with Time-dependent Coefficient

This paper discusses the initial inverse heat problem (backward heat problem) with time-dependent coefficient. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. Two regularization solutions of the backward heat problem will be given by a modified quasi-boundary value method. The Hölder type error estimates between the regularization...

Multiple time-dependent coefficient identification thermal problems with a free boundary

Stability for Time-Dependent Inverse Transport

This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from full knowledge of the albedo operator at the boundary of a bounded domain of interest. We present optimal stability results on the reconstruction of the absorption and scattering parameters for a given error in the measured albedo operator.