Accession Number : ADA116154
Title : The Riemann Problem in Two Space Dimensions for a Single Conservation Law.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Wagner,David H
PDF Url : ADA116154
Report Date : Apr 1982
Pagination or Media Count : 50
Abstract : Solutions are given for the partial differential equation with initial data constant in each quadrant of the (x,y) plane. This problem generalizes the Riemann Problem for equations in one space dimension. Although existence and uniqueness of solution are known, little is known concerning the qualitative behavior of solutions. When f and g are convex and f = g, then our solutions satisfy the uniqueness, or entropy conditions given by Kruzkov and Vol'pert. Under certain extra conditions on f and g, our solutions satisfy the entropy condition if f and g are convex and sufficiently close. A counterexample is given to show the necessity of these extra conditions on f and g. The correct entropy solution for this counter-example exhibits new and interesting phenomena.
Descriptors : *Partial differential equations, *Conservation, *Quadrants, Constants, Entropy, Shock waves, Nonlinear systems, Two dimensional, Value, Scalar functions
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE