JournalsaihpcVol. 30, No. 1pp. 141–155

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

  • Juan Campos

    Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

  • Pilar Guerrero

    Centre de Recerca Matemática, Campus de Bellaterra, Edifici C. 08193 Bellaterra, Barcelona, Spain

  • Óscar Sánchez

    Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

  • Juan Soler

    Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
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Abstract

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 classical regularity, but also the existence of discontinuous entropy traveling wave solutions.

Cite this article

Juan Campos, Pilar Guerrero, Óscar Sánchez, Juan Soler, On the analysis of traveling waves to a nonlinear flux limited reaction–diffusion equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 1, pp. 141–155

DOI 10.1016/J.ANIHPC.2012.07.001