On the global domain of influence of solutions with internal layers. (Q1432313)

The authors deal with the problem \[ \begin{gathered} \varepsilon^2 u_{xx}- u_t= f(u,x,\varepsilon),\quad (x,t)\in \Omega\times (0,+\infty),\tag{1}\\ u_x(a,t,\varepsilon)= u_x(b,t,\varepsilon)= 0,\quad t\in (0,+\infty),\tag{2}\\ u(x,0,\varepsilon)= u_0(x,\varepsilon),\quad x\in\overline\Omega,\tag{3}\end{gathered} \] where \(\varepsilon> 0\) is a small parameter and \(\Omega\equiv (a,b)\). Here the authors are mainly interested in the global domain of attraction of stationary solutions with internal layers for (1)--(3).