Shadowing matching errors for wave-front-like solutions (Q1923676)

The author deals with a singularly perturbed reaction-diffusion equation with a small parameter \(\varepsilon>0\) in one-dimensional space \(\varepsilon u_t=\varepsilon^2 u_{xx}+f(u,x,\varepsilon)\) \((x\in\mathbb{R}\), \(t\geq 0)\), where the unknown variable \(u\) is an \(\mathbb{R}^n\) valued function. He studies a new method of a construction of solution with (multiple) internal layers from a formal solution obtained by the matched asymptotic expansion.