Entire solutions with merging fronts to reaction-diffusion equations (Q854728)

This paper concerns the following reaction-diffusion equation \(u_t=u_{xx}+f(u)\) which has two stable constant equilibria and a monotone increasing traveling front solution connecting those equilibria. The authors prove that under certain assumptions there exists an entire solution such that for \(t\approx-\infty\) it behaves as two fronts on the left and right \(x\)-axes, while it converges to the above mentioned traveling front solution as \(t\to+\infty\).