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We consider in this paper a reaction-diffusion system under a KPP hypothesisin a cylindrical domain in the presence of a shear flow. Such systems arise inpredator-prey models as well as in combustion models with heat losses.Similarly to the single equation case, the existence of a minimal speed c* andof traveling front solutions for every speed c > c* has been shown both in thecases of heat losses distributed inside the domain or on the boundary. Here, wedeal with the accordance between the two models by choosing heat losses insidethe domain which tend to a Dirac mass located on the boundary. First, using thecharacterizations of the corresponding minimal speeds, we will see that theyconverge to the minimal speed of the limiting problem. Then, we will takeinterest in the convergence of the traveling front solutions of ourreaction-diffusion systems. We will show the convergence under some assumptionson those solutions, which in particular can be satisfied in dimension 2.

KPP reaction-diffusion systems with loss inside a cylinder: convergence toward the problem with Robin boundary conditions