Existence Of Solutions For A Single Time Delay Reaction Diffusion Equation Forward

In this paper, we study the existence of traveling wave fronts of continuous and spatially discrete reaction-diffusion models with a single delay respectively. The existence of such solutions is proved using the upper-lower solution technique.The whole paper consists of three chapters. In Chapter 1, we introduce some elementary concepts and results from the upper-lower solution theory. In Chapter 2, we consider reaction-diffusion equations with a single delay. Under the quasi-monotonicity and the weak quasi-monotonicity conditions, simple criterions are established for the existence of traveling wave fronts of reaction-diffusion equations with a single delay using the upper-lower solution technique. Some known results are generalized. In Chapter 3, we deal with the existence of traveling wave fronts of an age-structured spatially discrete reaction-diffusion model of a single species. We also show that the traveling wave front with the critical wave speed exists.