High amplitude solutions for small data in pairs of conservation laws that change type

• Type: Article in International Conference Proceedings Book
• Date: 2008

Authors

Vítor Matos (Author) FEP; Marchesin, D (Author) Other

Conference proceedings International

Title: HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS: PROCEEDINGS OF THE 11TH INTERNATIONAL CONFERENCE ON HYPERBOLIC PROBLEMS

Pages: 711-719

11th International Conference on Hyperbolic Problems

Lyon, FRANCE, JUL 17-21, 2006

Indexing

ISI Web of Knowledge - 2 Citations

Other information

Authenticus ID: P-00K-JCZ

DOI: 10.1007/978-3-540-75712-2_72

Abstract (EN): We prove that high amplitude Riemann solutions arise from Riemann data with arbitrarily small amplitude in the hyperbolic :region near the point where the rarefaction curves are tangent to the elliptic region. These solutions arise in a quadratic system of conservation laws with a compact elliptic region. The second-order terms in the fluxes correspond to type IV in Schaeffer and Shearer classification. For such Riemann data there is no small amplitude solution. Whitney perturbations of the fluxes do not change the result. Thus, we understand one possible consequence for violating strict hyperbolicity in the neighborhood of the Riernann data points. The violation of this hypothesis in Lax's renowned theorem may yield large amplitude solutions for small data.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 9