Stability of travelling waves for a cross-diffusion model (Q1378568)

The following coupled system of parabolic and ordinary differential equations is investigated: \[ u_t=\rho v-(v-1)^2u-s u+v_{xx}, \qquad v_t=u-hv, \] \((h, \rho, s= \text{const}>0)\). This system is a cross-diffusion model of a mono-species forest with two age classes. By using the theory of strongly continuous nonanalytic semigroups and a detailed spectral analysis, the asymptotic stability of travelling waves is established.