On the formation of a solution with an internal layer in a parabolic system with different Powers of a small parameter (Q1778271)

This paper concerns singularly perturbed parabolic systems of the type \[ \left.\begin{aligned}\varepsilon^2(u_{xx}- u_t) &= f(u,v,x,\varepsilon),\\ \varepsilon(v_{xx}- v_t) &= g(u,v,x,\varepsilon)\end{aligned}\right\}\;a< x< b \] with homogeneous Neumann boundary conditions. The authors obtain conditions on the initial functions and the nonlinearities \(f\) and \(g\) guaranteeing the existence of a nonstationary contrast step-like structure.