On the theory of alternating contrast structures (Q1571246)

The authors consider a singularly perturbed parabolic equation whose right-hand side is a periodic function of time in following form: \[ \varepsilon^2(u_{xx}-u_t)= F(u,x,t), \quad 0<x<1,\;-\infty<t<\infty, \] \[ u(0,t,\varepsilon)=u^0(t), \quad u(1,t,\varepsilon)=u^1(t). \] A solution varying from the purely boundary-layer type to the step-like type is investigated numerically and analytically. These investigations lead to results that agree well with numerical computations.