Accession Number : AD0469973
Title : UNIFORMISATION OF A QUASI-LINEAR HYPERBOLIC EQUATION, PART II, SOLUTION STRUCTURE IN THE LARGE.
Descriptive Note : Technical rept.,
Corporate Author : WISCONSIN UNIV-MADISON DEPT OF MATHEMATICS
Personal Author(s) : Meyer, Richard E.
Report Date : 30 MAR 1965
Pagination or Media Count : 24
Abstract : 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 Ludford's 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)
Descriptors : (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), (*BOUNDARY VALUE PROBLEMS, SPECIAL FUNCTIONS(MATHEMATICAL)), DIFFERENTIAL EQUATIONS, OCEAN BOTTOM TOPOGRAPHY, GAS FLOW, FLUID MECHANICS.
Distribution Statement : APPROVED FOR PUBLIC RELEASE