Periodic traveling curved fronts in reaction-diffusion equation with bistable time-periodic nonlinearity (Q630587)

Consider the reaction-diffusion equation \[ {\partial u\over \partial t}=\Delta u+f(u(x,y,t),t) \] for \((x,y)\in \mathbb{R}^2\) and \(t>0\). Assuming that \(f\) satisfies appropriate conditions on periodicity and bistable fixed points, and by constructing super- and subsolutions, the authors show the existence and the global stability of periodic traveling wave fronts for the equation.