A note on shocks in nonlinear similarity fields
Abstract
The authors derive a necessary and sufficient condition for the existence of similarity shocks for a system of two quasilinear, firstorder partial differential equations. These shocks, expressed as lines of discontinuity in the dependent variables across which appropriate jump conditions must be satisfied, comply with the similarity assumption and occur along similarity lines across which the correct jump conditions will be expressible in terms of similarity variables only. A procedure for deriving similarity shocks is applied to the small perturbation equation of twodimensional Cartesian and axisymmetric transonic flow.
 Publication:

Indiana University Mathematics Journal
 Pub Date:
 May 1976
 Bibcode:
 1976IUMJ...25..397G
 Keywords:

 Flow Equations;
 Nonlinear Equations;
 Partial Differential Equations;
 Shock Wave Propagation;
 Similarity Theorem;
 Nonlinear Systems;
 Small Perturbation Flow;
 Transonic Flow;
 Fluid Mechanics and Heat Transfer