Volume 14, Issue 4

We consider the inverse problem of determining dipole sources, by using boundary measurements. A local Lipshitz stability is established and a cost function transforming our inverse problem into an optimization one is proposed. This cost function involves the solutions computed from both the prescribed and measured data through their values inside the domain and not only on the boundary. An application to inverse EEG problem for which numerical experiments are performed for three concentric spheres representing the scalp, skull and brain as the model of the head, has been proposed.

We give some stability estimates for the inverse problem consisting in the determination of source term and coefficients which appear in an elliptic or parabolic equations and depend fully on all the components of variables, from boundary measurements.

In this paper, a boundary integral method is used to solve an inverse heat conduction problem. An algorithm for the inverse problem of the one dimensional case is given by using the fundamental solution. Numerical results show that our algorithm is effective.

The inverse problem of wave scattering for a system of data collected at the observation surface with multiple coverage of sources and receivers is considered. It is shown that this redundant data system is equivalent to the configuration studied previously, in which the receiver point coincides with the source point: in both cases the wave field continuation back in time reduces the scattering problem considered in a linearized approximation to the Cauchy problem (that with instantaneously actuated secondary field sources represented by sought-for inhomogeneities) in the reference medium with a "half" value of wave velocity.

An inverse problem to determine degenerate time- and space-dependent kernels of internal energy and heat flux by means of flux measurements is considered. Existence and uniqueness of a solution to the inverse problem are proved.

In this paper we discuss an inversion algorithm which combined with the L-curve criterion for the selection of the regularization parameter, effectively yields shape reconstructions of penetrable obstacles. The required scattered elastic field is generated by either a P or S-incident wave. In particular the improved variant of the linear sampling method (LSM), the so called ( F * F ) 1/4 -method is studied for the two dimensional elastic transmission case. For our reconstructions we assume that the far field data are noisy and we employ the L-curve for the selection of the regularization parameter. The location of the vertex of the L-curve yields an appropriate value of the regularization parameter. Furthermore, the L-curve approach does not require a priori knowledge of the noise level, and hence combined with the LSM can be used for real world reconstructions, in which noise in the data is unknown.