Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 149, pp. 1-17.
Title: Nonclassical shock waves of conservation laws:
Flux function having two inflection points
Authors: Ho Dac Nghia (International Univ., Ho Chi Minh, Vietnam)
Mai Duc Thanh (International Univ., Ho Chi Minh, Vietnam)
Abstract:
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.