Introduction

Classification groups P.D.E. with similar properties together.

Subsonic: smooth solutions, unlimited region of dependence, iterative solution. Supersonic: singularities, characteristic lines, spatial marching solution.

2D second order quasilinear equations:

a u_xx + 2 b u_xy + c u_yy + d = 0

where a=a(x,y,u,u_x,u_y), b=b(x,y,u,u_x,u_y), c=c(x,y,u,u_x,u_y), and d=d(x,y,u,u_x,u_y).

Classification:

• b² - ac > 0: hyperbolic
• b² - ac = 0: parabolic
• b² - ac < 0: eliptic

10/27/00 0:27:22