The role of convection in the limit shape of the critical front profile for Born-Infeld diffusion models

DOI10.1007/S00032-024-00397-6arXiv2306.13806OpenAlexW4396871634MaRDI QIDQ6441319

Mohamed Jleli, Maurizio Garrione, Bessem Samet

Publication date: 23 June 2023

Abstract: In this paper, we deal with models with Born-Infeld type diffusion and monostable reaction, investigating the effect of the introduction of a convection term on the limit shape of the critical front profile for vanishing diffusion. We first provide an estimate of the critical speed and then, through a careful analysis of an equivalent first-order problem, we show that different convection terms may lead either to a complete sharpening of the limit profile or to its complete regularization, presenting some related numerical simulations.

Full work available at URL: https://doi.org/10.1007/s00032-024-00397-6

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Traveling wave solutions (35C07) Quasilinear parabolic equations with mean curvature operator (35K93)

This page was built for publication: The role of convection in the limit shape of the critical front profile for Born-Infeld diffusion models

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6441319)