On a diffusion model with absorption and production

TL;DR

This paper analyzes radial solutions of superlinear elliptic equations modeling diffusion with both absorption and production, exploring their structure, asymptotic behavior, and effects of Hardy potentials, highlighting phenomena unique to reaction terms that change sign.

Contribution

It provides a detailed analysis of solutions with absorption and production, including their asymptotics and the impact of Hardy potentials, extending previous models.

Findings

Existence of unique radial solutions with specific asymptotic behaviors.

Identification of phenomena only occurring when absorption and production coexist.

Generalization of results to include Hardy potentials.

Abstract

We discuss the structure of radial solutions of some superlinear elliptic equations which model diffusion phenomena when both absorption and production are present. We focus our attention on solutions defined in R (regular) or in R \ {0} (singular) which are infinitesimal at infinity, discussing also their asymptotic behavior. The phenomena we find are present only if absorption and production coexist, i.e., if the reaction term changes sign. Our results are then generalized to include the case where Hardy potentials are considered.