A Review of Travelling Wave Solutions

In this paper we review the existence of diierent types of travelling wave solutions u(x; t) = (x ? ct) of degenerate non-linear reaction-diiusion equations of the form u t = D(u)u x ] x + g(u) for diierent density-dependent diiusion coeecients D and kinetic part g. These include the non-linear degenerate generalized Fisher-KPP and the Nagumo equations. Also, we consider an equation whose diiusion coeecient changes sign as the diiusive substance increases. This describes a diiusive-aggregative process. In this case the travelling wave solutions are explored and the ill-posedness of two boundary-value problems associated with the above equation is stated.