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 du df(u) , . m + ~oT9(o)' where (x,t) £lx R+,u = u(x,t) € R. The main new feature with respect to previous works is that the flux function / may have finitely many inflection points, intervals in which it is afEne, 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.