There has been considerable progress in recent years solving inverse problems for nonlinear hyperbolic equations. One of the striking aspects these developments is use nonlinearity to get new information, which not possible corresponding linear We illustrate this several examples including Einstein equations and elasticity among others.

The bidirectional wave transformation developed for scalar equations is shown to have interesting extensions for first-order hyperbolic systems. Assuming a localized waveform of the solution gives an equation for the envelope of the localized wave. The type of the envelope equation depends on the characteristics of the original hyperbolic equations, and the speed of the localized wave. This met...

Some aspects of recent developments in the study of the Euler equations for compressible fluids and related hyperbolic conservation laws are analyzed and surveyed. Basic features and phenomena including convex entropy, symmetrization, hyperbolicity, genuine nonlinearity, singularities, BV bound, concentration, and cavitation are exhibited. Global well-posedness for discontinuous solutions, incl...

The nonlocal boundary value problem for a hyperbolic-parabolic equation in a Hilbert space H is considered. The difference schemes approximately solving this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established. In applications, the stability estimates for the solutions of the difference schemes of the mixed type boundary val...