An elementary introduction to and analytic properties of some shock problems
Abstract
Several techniques for obtaining solutions to partial and ordinary differential equations for flow phenomena, particularly in the presence of a shock wave, are presented. One approach is to allow for piecewise smooth or other general functions. A second method is to consider small viscous or diffusive effects, which smears out shock effects. The solution of the second approach approximates the weak solution of the first method as the disturbance becomes arbitrarily small. The mathematical relationship between the two approaches is illustrated with an ordinary differential boundary value problem where conditions for the uniqueness of the solution are demonstrated.
 Publication:

IN: An introduction to computational and asymptotic methods for boundary and interior layers; Short Course
 Pub Date:
 1982
 Bibcode:
 1982icam.proc...46L
 Keywords:

 Computational Fluid Dynamics;
 Partial Differential Equations;
 Shock Waves;
 Unsteady Flow;
 Boundary Value Problems;
 Nonlinear Equations;
 Shock Discontinuity;
 Smoothing;
 Uniqueness Theorem;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer