Contrast structures of variable type in quasilinear parabolic equations (Q2388036)

The authors deal with the boundary value problem \(\varepsilon (u_{xx}-u_t)-A(u, x, t) u_x-B(u, x, t)=0\), \(u(a, t)=u(b, t)=0\), \(t\in {\mathbb R}\), \(x\in (a, b).\) The required function \(u\in C^{2, 1} ([a, b]\times {\mathbb R})\) satisfies the periodicity condition. The main goal of the paper is to study so called contrast structures arising between solutions to this problem (for example, step-like contrast structure).