Singular integral equations with applications to travelling waves for doubly nonlinear diffusion

Ecuaciones integrales singulares con aplicaciones a Travelling Waves en difusión doblemente no lineal

Équations intégrales singulières avec applications aux Travelling Waves pour diffusion doublement non linéaire

Alejandro Garriz (1, 2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IMAG - Institut Montpelliérain Alexander Grothendieck

The goal of this article is to offer a series of results related to the existence and properties of wavefront solutions for doubly nonlinear diffusion-reaction equations involving the p-Laplacian operator in terms of the constitutive functions of the problem. These results are derived from the analysis of singular Volterra integral equations that appear in the study of monotone travellingwave solutions for such equations. Our results extend the ones due to B. Gilding and R. Kersner for the case p = 2 to p > 1. The fact that p ̸ = 2 modifies the nature of the singularity in the integral equation, and introduces the need to develop some new tools and ideas for the analysis.

Mots clés: Singular Volterra integral equations; Doubly nonlinear reaction-diffusion equations; Travelling waves

Domaines: Equations aux dérivées partielles [math.AP]

Alejandro Garriz. Singular integral equations with applications to travelling waves for doubly nonlinear diffusion. 2022. ⟨hal-03621241⟩