TRAVELING WAVE SOLUTIONS FOR A ONE DIMENSIONAL MODEL OF CELL-TO-CELL ADHESION AND DIFFUSION WITH MONOSTABLE REACTION TERM

摘要

This work is concerned with the properties of the traveling wave solutions of a one dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion with net birth term ρ_t = [D(ρ)ρ_x]_x + g(p) t ≥ 0, x∈R, where D(ρ) may take positive or negative values with different population density ρ and adhesion coefficient α ∈ [0,1], and the negative one will lead to the ill-posedness of the equation. In all these cases we prove the existence of infinitely many traveling wave solutions, where these solutions are parameterized by their wave speed and monotonically connect the stationary states ρ = 0 and ρ=1.