Entropy solutions for linearly degenerate hyperbolic systems of rich type
✍ Scribed by Ta-Tsien Li; Yue-Jun Peng; Jérémy Ruiz
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 208 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0021-7824
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This paper deals with the global exact controllability for first-order quasilinear hyperbolic systems of diagonal form with linearly degenerate characteristics. When the system has no zero characteristics, we establish the global exact boundary controllability from one arbitrarily preassigned C 1 da
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## Abstract One often believes that there is no shock formation for the Cauchy problem of quasilinear hyperbolic systems (of conservation laws) with linearly degenerate characteristic fields. It has been a conjecture for a long time (see __Arch. Rational Mech. Anal.__ 2004; **172**:65–91; __Compres
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