Affiliations: Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain. E-mail: [email protected] | Institut für Mathematik. Universität Zürich, Zürich, Switzertland. E-mail: [email protected] | Basque Center for Applied Mathematics, Bizkaia Technology Park, Derio, Basque Country, Spain. E-mail: [email protected] | Ikerbasque – Basque Foundation for Science, Bilbao, Basque Country, Spain
Note: [] Corresponding author: Enrique Zuazua, Basque Center for Applied Mathematics, Bizkaia Technology Park, B.500 E48160, Derio, Basque Country, Spain. E-mail: [email protected].
Abstract: We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a non-local evolution one having a travelling wave solution with zero speed of propagation with exactly the same profile as the original one. This procedure allows us to compute simultaneously the travelling wave profile and its propagation speed avoiding moving meshes, as we illustrate with several numerical examples. We analyze the relation of the new equation with the original one in the entire real line. We also analyze the behavior of the non-local problem in a bounded interval with appropriate boundary conditions. We show that it has a unique stationary solution which approaches the traveling wave as the interval gets larger and larger and that is asymptotically stable for large enough intervals.
