Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4611937 | Journal of Differential Equations | 2009 | 20 Pages |
In this paper we study the existence and non-existence of travelling wave to parabolic system of the form at=axx−af(b), bt=Dbxx+af(b), with f a degenerate nonlinearity. In the context of an auto-catalytic chemical reaction, a is the density of a chemical species called reactant A, b that of another chemical species B called auto-catalyst, and D=DB/DA>0 is the ratio of diffusion coefficients, DB of B and DA of A, respectively. Such a system also arises from isothermal combustion. The nonlinearity is called degenerate, since f(0)=f′(0)=0. One case of interest in this article is the propagating wave fronts in an isothermal auto-catalytic chemical reaction of order with 1