Long-time behavior for the Kirchhoff diffusion problem with magnetic fractional Laplace operator

TL;DR

This paper investigates the long-term behavior of a Kirchhoff diffusion problem involving a magnetic fractional Laplace operator, proving that solutions do not blow up infinitely over time using potential well methods.

Contribution

It establishes the non-occurrence of infinite time blow-up for the problem, employing energy and Nehari functionals in the analysis.

Findings

Infinite time blow-up cannot occur for the problem

Utilizes potential well method with energy and Nehari functionals

Provides theoretical insight into the stability of solutions

Abstract

We consider a Kirchhoff-type diffusion problem driven by the magnetic fractional Laplace operator. The main result in this paper establishes that infinite time blow-up cannot occur for the problem. The proof is based on the potential well method, in relationship with energy and Nehari functionals.