Two-Dimensional Riemann Problem in Gas Dynamics

<p>The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860 great progress has been achieved in the one-dimensional case. However the two-dimensional case is substantially different. Although research interest in it has lasted more than a century it has yielded almost no analytical demonstration. It remains a great challenge for mathematicians.<br>This volume presents work on the two-dimensional Riemann problem carried out over the last 20 years by a Chinese group. The authors explore four models: scalar conservation laws compressible Euler equations zero-pressure gas dynamics and pressure-gradient equations. They use the method of generalized characteristic analysis plus numerical experiments to demonstrate the elementary field interaction patterns of shocks rarefaction waves and slip lines. They also discover a most interesting feature for zero-pressure gas dynamics: a new kind of elementary wave appearing in the interaction of slip lines-a weighted Dirac delta shock of the density function. <br> The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics clarifies the boundaries of interaction of elementary waves demonstrates the interesting spatial interaction of slip lines and proposes a series of open problems. With applications ranging from engineering to astrophysics and as the first book to examine the two-dimensional Riemann problem this volume will prove fascinating to mathematicians and hold great interest for physicists and engineers.</p>