A non-local quenching system with coupled and uncoupled singular absorption terms

TL;DR

This paper investigates a non-local diffusion system with singular absorption terms, establishing conditions for solutions and characterizing quenching behavior and rates.

Contribution

It provides necessary and sufficient conditions for existence of solutions and characterizes quenching phenomena based on absorption exponents.

Findings

Existence conditions for stationary and quenching solutions.

Characterization of simultaneous and non-simultaneous quenching.

Determination of quenching rates.

Abstract

In this paper we study a non-local diffusion system of two equations with both coupled and uncoupled singular absorption terms of the type $u^{-p}$. We prove that there exist necessary and sufficient conditions for the existence of both stationary and quenching solutions. We also characterize in terms of the exponents of the absorption terms when the quenching is simultaneous or non-simultaneous and obtain the quenching rates.