Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Two-dimensional Riemann problem for a single conservation law


Authors: Tong Zhang and Yu Xi Zheng
Journal: Trans. Amer. Math. Soc. 312 (1989), 589-619
MSC: Primary 35L65; Secondary 35L67
MathSciNet review: 930070
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The entropy solutions to the partial differential equation

$\displaystyle (\partial /\partial t)u(t,x,y) + (\partial /\partial x)f(u(t,x,y)) + (\partial /\partial y)g(u(t,x,y)) = 0,$

with initial data constant in each quadrant of the $ (x,y)$ plane, have been constructed and are piecewise smooth under the condition $ f''(u) \ne 0, g''(u) \ne 0, (f''(u)/g''(u))\prime \ne 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.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35L65, 35L67

Retrieve articles in all journals with MSC: 35L65, 35L67


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0930070-3
PII: S 0002-9947(1989)0930070-3
Article copyright: © Copyright 1989 American Mathematical Society