Oscillatory traveling wave solutions to an attractive chemotaxis system

We investigate global existence and long time behavior of solutions for PDE models of chemotaxis.  In particular, we study oscillatory traveling wave solutions to an attractive  chemotaxis system. The convective part of this system is of mixed-type. The oscillatory nature of the traveling wave comes from the fact that 
one far-field state is in the elliptic region and another in the hyperbolic region.  Such traveling wave solutions are shown to be linearly unstable.

Thackeray Hall 427