Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip.

(1.3) Zs = ∆t,xZ + f(t+ 2αs, x,Z). In this equation s plays the role of time, ∆t,xZ = Ztt+Zxx is a standard diffusion term and f represents a nonlinear source (reaction term), which travels in the direction of the unbounded variable with the constant speed −2α. Among the solutions of (1.3) of a particular interest are solutions of the form Z(s, t, x) = u(t + 2αs, x) (the travelling waves with velocity −2α). The profile