Abstract:The aim of the paper is to study qualitative behavior of solutions to equation $u_t +f(u)_x =g(u)$, where $(x,t)\in\R\times (0,+\infty)$, $u=u(x,t)\in\R$. The main new feature with respect to previous works is that the flux function $f$ can have finitely many inflections, intervals in which it is affine, and corner points. The function $g$ is supposed to be zero at 0 and 1, and positive in between.We prove existence of heteroclinic travelling waves connecting the two constant states for opportune choice of speeds. Finally we analyze the large-time behavior of the Riemann problem with values 0 and 1, showing convergence to one of the travelling waves. The speed of the limiting profile is explicitly characterized.

**Paper:**- Available as PostScript
**Title:**- Qualitative Behavior of Conservation Laws with Reaction Term and Nonconvex Flux
**Author(s):**- Corrado Mascia, <mascia@mat.uniroma1.it>
**Publishing information:**- submitted
**Comments:****Submitted by:**- <mascia@mat.uniroma1.it> February 27 1997.

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