Traveling waves for highly degenerate and singular reaction-diffusion-advection equations with discontinuous coefficients

2025/07/08 by Umberto Guarnotta, Guarnotta, Umberto, Cristina Marcelli +1
Computer Science · Mathematics · Medicine · #35C07 #35K57 #35K59 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Navier-Stokes equation solutions #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.2507.06027

openalex publication_date 2025/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are furnished. Under an additional hypothesis on the convection term, the set of admissible wave speeds is characterized in terms of the minimum wave speed, which is estimated through a double-sided bound.

Citations

• Traveling waves in reaction-diffusion-convection equations with combustion nonlinearity
• Wavefronts for degenerate diffusion-convection reaction equations with\n sign-changing diffusivity
• Singular integral equations with applications to travelling waves for doubly nonlinear diffusion
• Travelling wave behaviour arising in nonlinear diffusion problems posed\n in tubular domains
• Monotone wave fronts for (p, q)-Laplacian driven reaction-diffusion\n equations

Related

• Traveling waves in reaction-diffusion-convection equations with combustion nonlinearity
• Uniqueness and nonuniqueness of fronts for degenerate diffusion-convection reaction equations
• Wavefronts for degenerate diffusion-convection reaction equations with\n sign-changing diffusivity
• Coupled reaction-diffusion equations with degenerate diffusivity: wavefront analysis
• Singular integral equations with applications to travelling waves for doubly nonlinear diffusion