## Two-dimensional Riemann problem for a single conservation law

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- by Tong Zhang and Yu Xi Zheng PDF
- Trans. Amer. Math. Soc.
**312**(1989), 589-619 Request permission

## Abstract:

The entropy solutions to the partial differential equation \[ (\partial /\partial t)u(t,x,y) + (\partial /\partial x)f(u(t,x,y)) + (\partial /\partial y)g(u(t,x,y)) = 0,\] 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

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## Additional Information

- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**312**(1989), 589-619 - MSC: Primary 35L65; Secondary 35L67
- DOI: https://doi.org/10.1090/S0002-9947-1989-0930070-3
- MathSciNet review: 930070