Search results for "Inverse problem"

A Method of Conversion of some Coefficient Inverse Parabolic Problems to a Unified Type of Integral-Differential Equation

2011

Coefficient inverse problems are reformulated to a unified integral differential equation. The presented method of conversion of the considered inverse problems to a unified Volterra integral-differential equation gives an opportunity to distribute the acquired results also to analogous inverse problems for non-linear parabolic equations of different types.

1973

The direct and the inverse problem of the light scattering from dilute polymer solutions is solved for GAUssian coils at the theta point. Theoretical scattering functions and their derivatives are analytically calculated for the general gamma distribution of molecular weights as a function of the non-uniformity and the weight average molecular weight, and also for various ratios of the statistical segment length of the coil to the wave length of the scattered light. The asymptote and the tangent of P are obtained by analysing the operator in the ZIMM equation and their mutual position is compared in the angle range 150° to 180°. The scattering envelopes of microgel systems are analytically …

Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data

2013

The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated Neumann series to estimate $X_{V}$ and $X_{V}^{*}$, which provides a good approximation of $X_{V}^{*…