Non-adiabatic KPP fronts with an arbitrary Lewis number

We establish existence of travelling fronts in thermo-diffusive systems of the KPP type in a shear flow with an arbitrary Lewis number and a positive heat-loss at the boundary. We then prove that the leftover concentration behind the front is positive, and that it is small when the heat-loss is small. On the other hand, when the heat-loss approaches a critical value, the temperature becomes uniformly small. Finally, in the limit of large flow amplitudes A, we show that, depending on the flow structure, the infimum of the front speeds both may become 0 or grow linearly in A for A ≫ 1. 1 Introduction and main results Existence and qualitative properties of thermo-diffusive fronts in flows have been a subject of active research in the last few years: see [3, 23] for extensive overviews. The majority of the results have been obtained for a single reaction-diffusion equation of the form Tt + u · ∇T = ∆T + f(T)(1 − T)