Electron. J. Diff. Eqns., Vol. 2006(2006), No. 149, pp. 1-17.

Nonclassical shock waves of conservation laws: Flux function having two inflection points

Ho Dac Nghia, Mai Duc Thanh

We consider the Riemann problem for non-genuinely nonlinear conservation laws where the flux function admits two inflection points. This is a simplification of van der Waals fluid pressure, which can be seen as a function of the specific volume for a specific entropy at which the system lacks the non-genuine nonlinearity. Corresponding to each inflection point, A nonclassical Riemann solver can be uniquely constructed. Furthermore, two kinetic relations can be used to construct nonclassical Riemann solutions.

Submitted September 7, 2006. Published December 5, 2006.
Math Subject Classifications: 35L65, 76N10, 76L05.
Key Words: Conservation law; non-genuine nonlinearity; nonclassical solution; kinetic relation.

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Ho Dac Nghia
Horizon International Bilingual School
02 Luong Huu hanh, Pham Ngu Lao Ward
District 1, Ho Chi Minh City, Vietnam
email: dacnghia@yahoo.com
Mai Duc Thanh
Department of Mathematics
International University, Quarter 6
Linh Trung Ward, Thu Duc District
Ho Chi Minh City, Vietnam
email: mdthanh@hcmiu.edu.vn

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