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.
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