This work should serve as an introductory text for graduate students and researchers
working in the important area of partial differential equations with a focus on problems …

Some recent developments in the study of the Cauchy problem for the Euler equations for
compressible fluids are reviewed. The local and global well-posedness for smooth solutions …

We present numerical solutions of a two-dimensional Riemann problem for the unsteady
transonic small disturbance equations that provides an asymptotic description of the Mach …

We establish the existence of a global solution to a regular reflection of a shock hitting a
ramp for the pressure gradient system of equations. The set-up of the reflection is the same …

This paper numerically studies the dynamics of symmetrical wedge shock intersection under
sinusoidal supersonic oscillation conditions. The 15 symmetrical wedges are used as the …

We formulate and solve a transonic regular reflection problem for the unsteady transonic
small disturbance equation, using a free boundary problem approach. Our method applies …

The propagation of curved, nonlinear wavefronts and shock fronts are very complex
phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and …

We present numerical solutions of a two-dimensional inviscid Burgers equation which
provides an asymptotic description of the Mach reflection of weak shocks. In our numerical …

We propose a theory of weakly nonlinear multidimensional self-sustained detonations
based on asymptotic analysis of the reactive compressible Navier–Stokes equations. We …

We present numerical solutions of a two-dimensional Riemann problem for the
compressible Euler equations that describes the Mach reflection of weak shock waves. High …