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Estimate of the Time Rate of Entropy Dissipation for Systems of Conservation Laws

✍ Scribed by Michael Sever

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
506 KB
Volume
130
Category
Article
ISSN
0022-0396

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✦ Synopsis

A priori estimates for weak solutions of nonlinear systems of conservation laws remain in short supply. In this note we obtain an estimate of the rate of total entropy dissipation for initialΓ‚boundary value problems for such systems, of any dimension and in any number of space variables. The essential assumptions made are those of a strictly convex entropy density, an L estimate on the solution, and initial data of ``bounded variation'' as described here.

πŸ“œ SIMILAR VOLUMES

Uniqueness failure for entropy solutions
Uniqueness failure for entropy solutions of hyperbolic systems of conservation laws
✍ Michael Sever πŸ“‚ Article πŸ“… 1989 πŸ› John Wiley and Sons 🌐 English βš– 460 KB πŸ‘ 1 views

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

Correction to: β€œUniqueness failure for e
Correction to: β€œUniqueness failure for entropy solutions of hyperbolic systems of conservation laws”
✍ Michael Sever πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 112 KB πŸ‘ 1 views

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