Convergence rates to traveling waves for an FKPP model with nonlinear advection

We establish convergence rates of solutions to traveling waves for a reaction diffusion model with nonlinear advection. The convergence rate is proven using the shape defect function. We introduce a novel energy methods-based approach that uses a weighted Nash inequality to obtain $L^{\mathrm{\infty }}$-estimates on the shape defect function. In determining the convergence rates, we also establish the front location for the model.