Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem

Abstract

Abstract. In this work we consider the identifiability of two coefficients a(u) and c(x) in a quasilinear elliptic partial differential equation from observation of the Dirichlet-toNeumann map. We use a linearization procedure due to Isakov [18] and special singular solutions to first determine a(0) and c(x) for x ∈ Ω. Based on this partial result, we are then able to determine a(u) for u ∈ R by an adjoint approach.

Numerical identification of a nonlinear diffusion law via regularization in Hilbert scales

“…For the numerical solution, we employ a discretized version of the Tikhonov functional (16). The integral required for the data misfit term is approximated by numerical quadrature with 500 integration points and the required data h δ and y δ are computed by evaluation of the exact functions h and y on the corresponding integration points and by adding uniformly distributed random noise of size δ.…”

On an Inverse Problem for the Stationary Equation with a Boundary Condition of the Third Type

“…Let w y = a − u y . This function satisfies ( 11)-( 13) with y = k. Multiplying (11) for k = y by w y in terms of the inner product in L 2 (Ω) and integrating by parts in the first term, we obtain…”

“…Such problems arise in determination of unknown physical properties of a medium. In particular, the lowest coefficient k specifies, for instance, the catabolism of contaminants due to chemical reactions [10] or the absorption in diffusion and acoustic problems [11].…”

Inverse problems for the stationary and pseudoparabolic equations of diffusion

“…Applications of such problems deal with the recovery of unknown parameters indicating physical properties of a medium. In particular, the lowest coefficient k specifies, for instance, the catabolism of contaminants due to chemical reactions [6] or the absorption (also known as potential) in the diffusion and acoustics problems [7].…”