We consider the optimization approach to the acousto-electric imaging problem. Assuming that the electric conductivity distribution is a small perturbation of a constant, we investigate the least-squares estimate analytically using (multiple) Fourier series, and confirm the widely observed fact that acousto-electric imaging has high resolution and is statistically stable. We also analyze the case of partial data and the case of limited-view data, in which some singularities of the conductivity can still be imaged.

Difference approximations of hyperbolic partial differential equations with highly oscillatory coefficients and initial values are studied. Analysis of strong and weak convergence is carried out in the practically interesting case when the discretization step sizes are essentially independent of the oscillatory wave lengths. © 1993 John Wiley & Sons, Inc.

In this paper, we study the Li stability of perturbation of constant states for 2 x 2 systems of conservation laws. We introduce a nonlinear functional which is equivalent to the Li norm of the difference between the constant state and the approximate solutions consisting of elementary waves and is non-increasing in time for the limiting weak solution. This yields the Li stability of the constant states. The approximate solutions are constructed with the aid of wave tracing for the random choice method. Our functional reveals the aspects of nonlinear wave behavior, particularly the coupling of waves pertaining to different characteristic families, which affects the Li norm of the solutions.

The compressible Euler equations, which govern the gas flow surrounding a solid ball with mass M and frictional damping in n dimensions, t+(u)= 0,(u) t+ (u u)+ P ()=-Mx/| x| n-2u, where , u, P and M are the density, velocity, pressure and mass of the gas, respectively, n 3 is the dimension of x, and > 0 is the frictional constant, are examined. The pressure is assumed to satisfy the law and 12 , K is a positive constant. The existence and non-existence of global smooth solutions are studied for the initial boundary problem of the Euler equations.

This note studies the Monge-Ampère Keller–Segel equation in a periodic domain , a fully nonlinear modification of the Keller–Segel equation where the Monge-Ampère equation substitutes for the usual Poisson equation . The existence of global weak solutions is obtained for this modified equation. Moreover, we prove the regularity in for some .