Global influence domains of stable solutions with internal layers (Q2784550)

The authors consider the family of reaction-diffusion Neumann-Cauchy problems NEWLINE\[NEWLINE\varepsilon^2u_{xx} - u_t = f(u, x, \varepsilon),\quad (x, t)\in ]a, b[\times\mathbb{R}_+,NEWLINE\]NEWLINE NEWLINE\[NEWLINEu_x(a, t, \varepsilon)=u_x (b,t,\varepsilon)=0,\quad t\in\mathbb{R}_+,NEWLINE\]NEWLINE NEWLINE\[NEWLINEu(x,0,\varepsilon)=u_0(x, \varepsilon),\quad x\in ]a, b[,NEWLINE\]NEWLINE where the nonlinearity has two stable zeros. Under some special conditions it was easy shown the existence of a stable stationary solution with internal transition layer. The main result is the study of the influence domain of such solution.