Bistable traveling waves for time periodic reaction-diffusion equations in strip with Dirichlet boundary condition

We study the existence of bistable traveling wave solutions for time periodic reaction-diffusion equations in straight strips subject to the Dirichlet boundary condition. We first employ a monotone dynamical system framework to establish the existence of such a wave by assuming a bistability structure in terms of multiplicity and stability of periodic solutions in the section of the strip, which is then realized under a set of sufficient explicit conditions; in particular, the bistability structure appears if the reaction term is a time periodic smooth perturbation of the nonlinearity λu(1−u)(u−a) when a∈(0,1/2) and λ>λ_⁎ for some λ_⁎>0.