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arXiv · 1402.1679

Qualitative behavior for flux-saturated mechanisms: Traveling waves, waiting time and smoothing effects

Juan Calvo·Juan Campos·Vicent Caselles·Oscar Sánchez·Juan Soler
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Abstract

This paper is devoted to the analysis of qualitative properties of flux-saturated type operators in dimension one. Specifically, we study regularity properties and smoothing effects, discontinuous interfaces, the existence of traveling wave profiles, sub- and super-solutions and waiting time features. The aim of the paper is to better understand these kind of phenomena throughout two prototypic operators: The relativistic heat equation and the porous media flux-limited equation. As an important consequence of our results we deduce that solutions to the one-dimensional relativistic heat equation become smooth inside their support on the long time run.

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Juan Calvo, Juan Campos, Vicent Caselles, Oscar Sánchez, Juan Soler. 2014-03-10. Qualitative behavior for flux-saturated mechanisms: Traveling waves, waiting time and smoothing effects. https://doi.org/10.4171/jems%2F670

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