UNIFORMISATION OF A QUASI-LINEAR HYPERBOLIC EQUATION, PART II, SOLUTION STRUCTURE IN THE LARGE.
WISCONSIN UNIV-MADISON DEPT OF MATHEMATICS
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The concepts of regular variables and formal solutions are used to study the limit lines of the Generalized Cauchy Problem for a typical system of homogeneous differential equations in two independent and two dependent variables. These lines are of physical interest on account of their relation to bore-formation in oceanographical applications and shock-formation in gas dynamical applications and of mathematical interest on account of their relation to the breakdown of classical existence theorems. It is shown that a singular point in the regular plane corresponding to a limit point cannot be isolated and a singular curve cannot end in the interior of the domain of the solution. A generalisation and new proof are given for Ludfords theorem that any nontrivial solution possesses limit points, if it is continued far enough. It is stressed that these results concern domains extending beyond that on which a solution is uniquely determined. Author