Radial equivalence and applications to the qualitative theory for a class of non-homogeneous reaction-diffusion equations

2022/12/20 by Razvan Gabriel Iagar, Iagar, Razvan Gabriel, Ariel Sánchez +1
Mathematics · Medicine · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2212.10644

openalex publication_date 2022/12/20 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28

Abstract

Some transformations acting on radially symmetric solutions to the following class of non-homogeneous reaction-diffusion equations |x|^σ₁∂_tu=Δu^m+|x|^σ₂u^p, (x,t)∈\real^N×(0,∞), which has been proposed in a number of previous mathematical works as well as in several physical models, are introduced. We consider here m≥1, p≥1, N≥1 and σ₁, σ₂ real exponents. We apply these transformations in connection to previous results on the one hand to deduce general qualitative properties of radially symmetric solutions and on the other hand to construct self-similar solutions which are expected to be patterns for the dynamics of the equations, strongly improving the existing theory. We also introduce mappings between solutions which work in the semilinear case m=1.

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