Partial differential equations are a many-faceted subject. Created to describe the
mechanical behavior of objects such as vibrating strings and blowing winds, it has …

During the production lifecycle of a reservoir, absolute permeability at any given location
may change in response to an increase in the net effective stress and a concomitant …

An obstacle in the use of Evans function theory for stability analysis of traveling waves
occurs when the spectrum of the linearized operator about the wave accumulates at the …

The eigenstructure of the equations governing one-dimensional ideal magnetohy-
drodynamics is examined, motivated by the wish to exploit it for construction of high …

The Riemann problem for a general inhomogeneous system of conservation laws is solved
in a neighborhood of a state at which one of the nonlinear waves in the problem takes on a …

We describe an extension of higher order Godunov methods to general systems of
hyperbolic conservation laws. This extension allow the method to be applied to problems …

In this paper we develop a first‐order system of conservation laws for finite deformation in
solids, describe its characteristic structure, and use this analysis to develop a second‐order …

In this paper, the issue of postshock oscillations generated by shock-capturing schemes is
investigated. Although these oscillations are frequently small enough to be ignored, there …

In this paper we examine the mathematical structure of a model for three-phase,
incompressible flow in a porous medium. We show that, in the absence of diffusive forces …

A new class of fundamental waves arises in conservation laws that are not strictly
hyperbolic. These waves serve as transitions between wave groups associated with …