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

VL - 312

SP - 559

EP - 619

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -