Traveling wave analysis for a mathematical model of malignant tumor invasion

This paper is concerned with traveling wave solutions to a malignant tumor invasion model. In 1999, Perumpanani et al. presented a mathematical model of malignant tumor cell invasion into connective tissue without cell diffusion. In their and subsequent researches, traveling waves have been studied mainly by numerical methods. In this paper, the existence of smooth traveling wave solutions to the model is proved rigorously. In order to show the existence of traveling waves, one considers heteroclinic orbits on a phase plane and constructs an invariant region for the orbits. Moreover, their asymptotic behavior is investigated. Finally, a remark on discontinuous traveling waves is given.