Microlocal analysis of a seismic linearized inverse problem. Abstract: The seismic inverse problem is to determine the wavespeed c(x) in the interior of a medium from measurements at the boundary. In this paper we analyze the linearized inverse problem in general acoustic media. The problem is to nd a left inverse of the linearized forward map F, or, equivalently, to nd the inverse of the norma...

A sequence of approximate linear collision models for hard-sphere and inverse-power-law gases is introduced. These models are obtained by expanding the linearized Boltzmann collision operator into a Hermite series, and a practical algorithm is proposed for evaluating the coefficients in the series. The sequence approximates the linearized Boltzmann operator to high accuracy, and it establishes ...

In this paper, it is shown that the linearized Boltzmann-Enskog collision operator cannot be dissipative in the L2-space setting contrarily to the linearized Boltzmann operator. Some estimates useful for the spectral theory are given. The Enskog equation is a modification of the Boltzmann kinetic equation, in which each particle is considered as a hard sphere with nonzero diameter a > 0 (and th...

‎Using the explicit forms of eigenstates for linearized operator related to a matrix version of Nonlinear Schrödinger equation‎, ‎soliton perturbation theory is developed for the $F=1$ bright spinor Bose-Einstein condensates‎. ‎A small disturbance of the integrability condition can be considered as a small correction to the integrable equation‎. ‎By choosing appropriate perturbation‎, ‎the soli...

The linearized problem around a time-periodic parallel flow of the compressible Navier-Stokes equation in an infinite layer is investigated. By using the Floquet theory, spectral properties of the evolution operator associated with the linearized problem are studied in detail. The Floquet representation of low frequency part of the evolution operator, which plays an important role in the study ...

This work deals with the focusing Nonlinear Schrödinger Equation in one dimension with pure-power nonlinearity near cubic. We consider the spectrum of the linearized operator about the soliton solution. When the nonlinearity is exactly cubic, the linearized operator has resonances at the edges of the essential spectrum. We establish the degenerate bifurcation of these resonances to eigenvalues ...