Geodesic
On the analysis of traveling waves to a nonlinear flux limited reaction–diffusion equation
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 1, pp. 141-155

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In this paper we study the existence and qualitative properties of traveling waves associated with a nonlinear flux limited partial differential equation coupled to a Fisher–Kolmogorov–Petrovskii–Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C 2 classical regularity, but also the existence of discontinuous entropy traveling wave solutions.

DOI : 10.1016/j.anihpc.2012.07.001
Classification : 35K55, 35B10, 35B40, 35K57, 35K40
Keywords: Flux limited, Relativistic heat equation, Singular traveling waves, Nonlinear reaction–diffusion, KPP, Traveling waves, Optimal mass transportation, Entropy solutions, Complex systems, Traffic flow, Biomathematics 
@article{AIHPC_2013__30_1_141_0,
     author = {Campos, Juan and Guerrero, Pilar and S\'anchez, \'Oscar and Soler, Juan},
     title = {On the analysis of traveling waves to a nonlinear flux limited reaction{\textendash}diffusion equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {141--155},
     publisher = {Elsevier},
     volume = {30},
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     year = {2013},
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     zbl = {1263.35059},
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     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.07.001/}
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Campos, Juan; Guerrero, Pilar; Sánchez, Óscar; Soler, Juan. On the analysis of traveling waves to a nonlinear flux limited reaction–diffusion equation. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 1, pp. 141-155. doi: 10.1016/j.anihpc.2012.07.001

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