The wave propagation in a one-dimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrijdinger equation d2$/dx2 + k211, = k2P(x)II, + Q(x)Jt with an added potential proportional to energy. The scattering and bound-state solutions of this equation are studied and the properties of the ...

The nonhomogeneous gas or fluid flowing through a nonhomogeneous porous medium is studied. An interesting phenomenon is discussed which shows that the state of the flow is not affected by the surrounding environment if some hypotheses are made on the porosity of the gas, the viscosity, and the permeability of the medium. Such a state is called an isolated environment. The conditions under which...

We begin with the initial-boundary-value problem for a coupled system of partial differential equations which describes the Biot consolidation model in poroelasticity. Existence, uniqueness and regularity theory is developed for the quasi-static case as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics...

The eigenvalues and eigenspaces of some discrete divand curl-related operators are investigated. The discrete operators give some good discrete analogues of the continuous counterparts and play an important role in developing finite volume schemes for solving div-curl equations and electromagnetic systems. Knowledge of the eigenvalues and eigenspaces is very useful in the numerical analysis of ...

Boundary contact problems of statics of the moment (couplestress) theory of elasticity are studied in the case of a unilateral contact of two elastic anisotropic nonhomogeneous media. A problem, in which during deformation the contact zone lies within the boundaries of some domain, and a problem, in which the contact zone can extend, are given a separate treatment. Concrete problems suitable fo...

In systems composed of water and hydrocarbons, Van der Waals interactions are dominated by the nonretarded, classical (Keesom) part of the Lifshitz interaction; the interaction is screened by salt and extends over mesoscopic distances of the order of the size of the (micellar) constituents of complex fluids. We show that these interactions are included intrinsically in a recently introduced loc...