2024/06/25 by Pavel Drábek, Drábek, Pavel, Michaela Zahradníková +1 · 1 citation
Computer Science · Mathematics · Medicine · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2406.17410
openalex publication_date 2024/06/25 · openalex created_date 2024/06/27 · openalex updated_date 2026/07/28
This paper concerns the existence and properties of traveling wave solutions to reaction-diffusion-convection equations on the real line. We consider a general diffusion term involving the p-Laplacian and combustion-type reaction term. We extend and generalize the results established for p=2 to the case of singular and degenerate diffusion. Our approach allows for non-Lipschitz reaction as well. We also discuss the shape of the traveling wave profile near equilibria, assuming power-type behavior of the reaction and diffusion terms.