The diffusive logistic model with a free boundary and seasonalsuccession

This paper concerns a diffusive logistic equation with a freeboundary and seasonal succession, which is formulated to investigatethe spreading of a new or invasive species, where the free boundaryrepresents the expanding front and the time periodicity accounts forthe effect of the bad and good seasons. The condition to determinewhether the species spatially spreads to infinity or vanishes at afinite space interval is derived, and when the spreading happens,the asymptotic spreading speed of the species is also given. Theobtained results reveal the effect of seasonal succession on thedynamical behavior of the spreading of the single species.