Propagation Phenomena for a Lotka–Volterra Cooperative Model with Degenerate Diffusion Under Climate Change

This paper is concerned with a Lotka–Volterra cooperative model with degenerate diffusion under climate change. Firstly, by constructing the appropriate upper and lower solutions to overcome the influence of the degeneracy and nonautonomous terms, and applying the monotone iteration method, we prove the existence of forced traveling waves with any speed \(c>0\) $c>0$ at which the habitat edge is shifting. Then based on the new comparison theorem for degenerate diffusion systems, we obtain the global existence of \(C^{\alpha ,\beta }\) $C^{\alpha ,\beta }$ -solution to the initial value problem of this system via the compactness analysis. At the end of the paper, some numerical simulations are conducted.