Herrero García, Miguel ÁngelEsquinas Candenas, Jesús2023-06-202023-06-2019900036-141010.1137/0521007https://hdl.handle.net/20.500.14352/57872We consider the semilinear system (S) ut−uxx+vp=0, vt−vxx+uq=0(−∞<x<+∞,t>0) with p>0 and q>0. We seek nonnegative and nontrivial travelling wave solutions to (S): u(x,t)=φ(ct−x), v(x,t)=ψ(ct−x) possessing sharp fronts, i.e., such that φ(ξ)=ψ(ξ)=0 for ξ≤ξ0 and some finite ξ0, which after a phase shift can always be assumed to be located at the origin. These solutions are called finite travelling waves (FTW). Here we show that if pq<1, for any real c there exists an FTW that is unique up to phase translations and unbounded, whereas no FTW exists if pq≥1. The asymptotic wave profiles near the front as well as far from it are also determined.journal articlehttps://doi.org/10.1137/0521007http://epubs.siam.orgmetadata only access517.9517.956.4Semilinear diffusion systemsTravelling wavesFrontsAsymptotic behaviourTravelling wave solutionsExistenceUniquenessNonexistenceEcuaciones diferenciales1202.07 Ecuaciones en Diferencias