Hyperbolic traveling waves driven by growth

Emeric Bouin 1, 2 Vincent Calvez 1, 2, * Grégoire Nadin 3
* Corresponding author
2 NUMED - Numerical Medicine
UMPA-ENSL - Unité de Mathématiques Pures et Appliquées, Inria Grenoble - Rhône-Alpes
Abstract : We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ ($\epsilon>0$), and proliferate according to a reaction term of monostable type. We study the existence and stability of traveling fronts. We exhibit a transition depending on the parameter $\epsilon$: for small $\epsilon$ the behaviour is essentially the same as for the diffusive Fisher-KPP equation. However, for large $\epsilon$ the traveling front with minimal speed is discontinuous and travels at the maximal speed $\epsilon^{-1}$. The traveling fronts with minimal speed are linearly stable in weighted $L^2$ spaces. We also prove local nonlinear stability of the traveling front with minimal speed when $\epsilon$ is smaller than the transition parameter.
Document type :
Journal articles
Complete list of metadatas

Contributor : Vincent Calvez <>
Submitted on : Monday, November 21, 2016 - 9:39:24 AM
Last modification on : Tuesday, November 19, 2019 - 11:44:52 AM
Long-term archiving on : Monday, March 20, 2017 - 4:50:46 PM


Files produced by the author(s)



Emeric Bouin, Vincent Calvez, Grégoire Nadin. Hyperbolic traveling waves driven by growth. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014, 24 (6), http://www.worldscientific.com/doi/abs/10.1142/S0218202513500802. ⟨10.1142/S0218202513500802⟩. ⟨hal-00632597v2⟩



Record views


Files downloads