A nonconvex scalar conservation law with trilinear flux

The focus of this paper is on traveling wave solutions of the equation u(t) + f(u)(x) = epsilonu(xx) + epsilon2 gammau(xxx), in which the flux function f is trilinear and nonconvex. In particular, it is shown that for combinations of parameters in certain ranges, there are t raveling waves that converge as epsilon --> 0 to undercompressive shocks, i n which the characteristics pass through the shock. The analysis is based o n explicit solutions of the piecewise linear ordinary differential equation satisfied by traveling waves. The analytical results are illustrated by nu merical solutions of the Riemann initial value problem, and are compared wi th corresponding explicit results for the case of a cubic flux function.