Geodesic
Qualitative behaviour for flux-saturated mechanisms: travelling waves, waiting time and smoothing effects
Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 441-472.

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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 travelling wave profiles, sub- and supersolutions and waiting time features. The aim of the paper is to better understand these phenomena through 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 in the long time run.
DOI : 10.4171/jems/670
Classification : 35-XX, 34-XX, 37-XX, 70-XX
Keywords: Flux limitation, flux-saturation, porous media equations, waiting time, pattern formation, travelling waves, optimal mass transportation, entropy solutions, relativistic heat equation, complex systems 
@article{JEMS_2017_19_2_a3,
     author = {Juan Calvo and Juan Campos and Vicent Caselles and \'Oscar S\'anchez and Juan Soler},
     title = {Qualitative behaviour for flux-saturated mechanisms: travelling waves, waiting time and smoothing effects},
     journal = {Journal of the European Mathematical Society},
     pages = {441--472},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2017},
     doi = {10.4171/jems/670},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/670/}
}
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Juan Calvo; Juan Campos; Vicent Caselles; Óscar Sánchez; Juan Soler. Qualitative behaviour for flux-saturated mechanisms: travelling waves, waiting time and smoothing effects. Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 441-472. doi : 10.4171/jems/670. http://geodesic.mathdoc.fr/articles/10.4171/jems/670/

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