Isolated singularities of solutions of a 2-D diffusion equation with mixed reaction

TL;DR

This paper investigates the local behavior and existence of solutions with isolated singularities for a specific 2-D diffusion equation involving mixed reaction terms, focusing on positive solutions near singular points.

Contribution

It provides new insights into the existence and local properties of solutions with isolated singularities for a nonlinear 2-D diffusion equation with mixed reaction terms.

Findings

Existence of solutions with isolated singularities established.

Characterization of local behavior near singularities.

Conditions on parameters for singular solutions.

Abstract

We study the local properties of positive solutions of the equation $-\Delta u+ae^{bu}=m|\nabla u|^q$ in a punctured domain $\Omega\setminus\{0\}$ of $\bf R^2$ where $m,a,b$ are positive parameters and $q>1$. We study particularly the existence of solutions with an isolated singularity and the local behaviour of such singular solutions.