TY - JOUR
T1 - Two-dimensional riemann problem for a single conservation law
AU - Zhang, Tong
AU - Zheng, Yuxi
N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 1989/4
Y1 - 1989/4
N2 - The entropy solutions to the partial differential equation (∂/∂t)u(t, x, y) + (∂/∂x)f(u(t, x, y)) + (∂/∂y)g(u(t, x, y)) = 0, with initial data constant in each quadrant of the (x, y) plane, have been constructed and are piecewise smooth under the condition f"(u) ≠ 0, g"(u) ≠ 0, (f"(u)lg"(u))' ≠ 0. This problem generalizes to several space dimensions the important Riemann problem for equations in one-space dimension. Although existence and uniqueness of solutions are well known, little is known about the qualitative behavior of solutions. It is this with which we are concerned here.
AB - The entropy solutions to the partial differential equation (∂/∂t)u(t, x, y) + (∂/∂x)f(u(t, x, y)) + (∂/∂y)g(u(t, x, y)) = 0, with initial data constant in each quadrant of the (x, y) plane, have been constructed and are piecewise smooth under the condition f"(u) ≠ 0, g"(u) ≠ 0, (f"(u)lg"(u))' ≠ 0. This problem generalizes to several space dimensions the important Riemann problem for equations in one-space dimension. Although existence and uniqueness of solutions are well known, little is known about the qualitative behavior of solutions. It is this with which we are concerned here.
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U2 - 10.1090/S0002-9947-1989-0930070-3
DO - 10.1090/S0002-9947-1989-0930070-3
M3 - Article
AN - SCOPUS:84966244791
SN - 0002-9947
VL - 312
SP - 559
EP - 619
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -