Periodic pyramidal traveling fronts of bistable reaction-diffusion equations with time-periodic nonlinearity (Q657461)

To study multidimensional traveling waves, the authors consider the following non-autonomous reaction-diffusion equation \[ {\partial u(\mathbf{y},t)\over \partial t}=\Delta u(\mathbf{y},t)+f(u(\mathbf{y},t),t) \] for \(\mathbf{y}\in \mathbb{R}^N\), where \(f(\cdot,t)\) is assumed to be periodic in \(t\). Under certain conditions on \(f\), the existence, uniqueness and stability of periodic pyramidal traveling fronts are proved for \(N=3\) while the existence is proved for \(N\geq 4\). These results extend recent results on \(V\)-shaped traveling fronts for \(N=2\) and pyramidal traveling fronts of autonomous equations for \(N\geq 2\).