On the analysis of traveling waves to a nonlinear flux limited reaction–diffusion equation
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 1, p. 141-155
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 : https://doi.org/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--diffusion equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {30},
     number = {1},
     year = {2013},
     pages = {141-155},
     doi = {10.1016/j.anihpc.2012.07.001},
     zbl = {1263.35059},
     mrnumber = {3011295},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2013__30_1_141_0}
}
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, Volume 30 (2013) no. 1, pp. 141-155. doi : 10.1016/j.anihpc.2012.07.001. http://www.numdam.org/item/AIHPC_2013__30_1_141_0/

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