Curvature dependences of wave propagation in reaction–diffusion models

Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of wave fronts. These have important applications many physical, ecological, and biological systems. In this work, we analyse dependences travelling fronts single reaction-diffusion equation with general reaction term. We derive an exact, non-perturbative dependence speed arises from transverse diffusion occurring parallel to front. Inward-propagating are characterised by three phases: establishment phase dominated initial boundary conditions, travelling-wave-like which normal velocity matches standard results singular perturbation theory, dip-filling where collision interaction create additional their progression rate. these behaviours using combination asymptotic analyses numerical simulations.