Travelling wave solutions for a nonlocal dispersal HIV infection dynamical model

This paper is devoted to developing a nonlocal dispersal HIV infection dynamical model. The existence of travelling wave solutions is investigated by employing Schauder's fixed point theorem. That is, we study the existence of travelling wave solutions for R0>1 and each wave speed c>c⁎. In addition, the boundary asymptotic behaviour of travelling wave solutions at +∞ is obtained by constructing suitable Lyapunov functions and employing Lebesgue dominated convergence theorem. By employing a limiting argument, we investigate the existence of travelling wave solutions for R0>1 and c=c⁎. The main difficulties are that the semiflow generated by the model does not have the order-preserving property and the solutions lack of regularity.