Qualitative behavior of conservation laws with reaction term and nonconvex flux

The aim of the paper is to study qualitative behavior of solutions to the equation partial derivativeu/partial derivativet + partial derivativef(u)/partial derivativex = g(u), where (x, t) is an element of R x R+, u = u(x, t) is an element of R. The main new feature with respect to previous works is that the flux function f may have finitely many inflection points, 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.