We consider a nonlinear system of conservation laws, which is strictly hyperbolic, genuinely nonlinear in the large, equipped with a convex entropy function and global Riemann invariants. Nevertheless, for such a system of dimension five, it is shown that uniqueness of the similarity solution of a R
Existence and uniqueness of solutions for some hyperbolic systems of conservation laws
β Scribed by Arnaud Heibig
- Publisher
- Springer
- Year
- 1994
- Tongue
- English
- Weight
- 1018 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0003-9527
No coin nor oath required. For personal study only.
β¦ Synopsis
We study the Cauchy problem for systems of conservation laws which belong to the Temple class. The compensated-compactness theory is used to prove existence of solutions. Some uniqueness results are established by means of Holmgren's principle.
π SIMILAR VOLUMES
The proof of Theorem 4.1 requires correction. The theorem is correct as stated, and the basic method of proof is valid. Only the method for making det A' negative is erroneous. Before giving the details, we make several general comments. The linear transformation (in particular valid for weak solu
Here u is the specific volume, u = I/p, p is the density and u is the speed of the gas. The equation of state of the gas is p ( v ) = k2/uY, where y is a constant, y = 1 + 2 ~, and E will be a small positive constant throughout this paper. We consider the initial value problem for (1) in the region
## Communicated by B. Brosowski A system of quasi-linear fint-order equations written in the divergence form and constrained by the unilateral differential inequality (the second law of thermodynamics) with a strictly m m v e entropy function is analysed. In the class BV, i.e. a subset of regular