On the analysis of traveling waves to a nonlinear flux limited reaction–diffusion equation

Campos, Juan; Guerrero, Pilar; Sánchez, Óscar; Soler, Juan

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 1, pp. 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.

Classification : 35K55, 35B10, 35B40, 35K57, 35K40
Mots clés : Flux limited, Relativistic heat equation, Singular traveling waves, Nonlinear reaction–diffusion, KPP, Traveling waves, Optimal mass transportation, Entropy solutions, Complex systems, Traffic flow, Biomathematics

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