---
abstract: 'In this paper we consider a model for the diffusion of a population in a strip-shaped field, where the growth of the species is governed by a Fisher-KPP equation and which is bounded on one side by a road where the species can have a different diffusion coefficient. Dirichlet homogeneous boundary conditions are imposed on the other side of the strip. We prove the existence of an asymptotic speed of propagation which is greater than the one of the case without road and study its behavior for small and large diffusions on the road. Finally we prove that, when the width of the strip goes to infinity, the asymptotic speed of propagation approaches the one of an half-plane bounded by a road, case that has been recently studied in [@BRR1; @BRR2].'
author:
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    Andrea Tellini\
    \
    \
    \
    `andrea.tellini@ehess.fr`
title: '**Propagation speed in a strip bounded by a line with different diffusion**[^1]'
---

*In memory of Giuliano Bardi (1948–2012),\
the one who taught me what a derivative is.*

**Keywords:** KPP equations, reaction-diffusion systems, 1D-2D systems, asymptotic speed of propagation.

**2010 MSC:** 35K57, 35B40, 35K40, 35B53.

Introduction {#sec1}
============

Recently, in [@BRR1], the system $$\label{11}
  \left\{ \begin{array}{lll}
  \!\!\!u_t(x,t)\!-\!Du_{xx}(x,t)\!=\!\nu 