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
Uniqueness of Classical and Nonclassical Solutions for Nonlinear Hyperbolic Systems
β Scribed by Paolo Baiti; Philippe G. LeFloch; Benedetto Piccoli
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 182 KB
- Volume
- 172
- Category
- Article
- ISSN
- 0022-0396
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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
## Abstract This paper is concerned with the asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems with linearly degenerate characteristic fields. Based on the existence results of global classical solutions, we prove that when __t__ tends to infinity,
The uniqueness for unbounded classical solutions of the magnetohydrodynamic (MHD) equations in the whole space is investigated. Under suitable growth condition, it is shown that the solution to the initial value problem is unique.
## Abstract In this paper, we first consider the Cauchy problem for quasilinear strictly hyperbolic systems with weak linear degeneracy. The existence of global classical solutions for small and decay initial data was established in (__Commun. Partial Differential Equations__ 1994; **19**:1263β1317