Recovery of interior eigenvalues from reduced near field data

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The domain can be arbitrarily small but fixed.The scattered waves are measured on the same surface. An effective procedure is suggested for recovery of interior eigenvalues by these data

Cal Poly Week of Welcome Expands Student Education Program

A mathematical model of general gas emitting systems is derived, and a sample of relevant mathematical results is offered. The present paper indicates that shallow subsurface gas sources in typical volcanic areas can be located if appropriate physico-chemical measurements are made on the Earth’s surface and put to use

Singular Localised Boundary-Domain Integral Equations of Acoustic Scattering by Inhomogeneous Anisotropic Obstacle

We consider the time-harmonic acoustic wave scattering by a bounded anisotropic inhomogeneity embedded in an unbounded anisotropic homogeneousmedium. The materialparametersmay have discontinuitiesacross the interfacebetween the inhomogeneous interior and homogeneous exterior regions. The corresponding mathematicalproblemis formulatedas a transmissionproblemsfora secondorderelliptic partial differential equation of Helmholtz type with discontinuous variable coefficients. Using a localised quasi-parametrix based on the harmonic fundamental solution, the transmission problem for arbitrary values of the frequency parameter is reduced equivalently to a system of singular localised boundary-domain integral equations. Fredholm properties of the corresponding localised boundarydomainintegral operatorarestudiedanditsinvertibilityisestablishedinappropriate Sobolev-Slobodetskii and Bessel potential spaces, which implies existence and uniquenessresults for the localised boundary-domainintegralequationssystem and the correspondingacoustic scattering transmission problem