Existence and uniqueness of traveling wave front of a nonlinear singularly perturbed system of reaction-diffusion equations with a Heaviside step function

The main purpose of this paper is to show the existence and uniqueness of a traveling wave front (U,W)=(U(x+v(ε)t),W(x+v(ε)t)) of the following nonlinear singularly perturbed system of reaction-diffusion equations with a Heaviside step function{∂u∂t=∂2u∂x2+2(H(u−θ)−u)−w,∂w∂t=∂2w∂x2+ε(u−w).