The Kirchhoff-type diffusion problem driven by a magnetic fractional Laplace operator

Abstract

In this work, we investigate the existence of local and global weak solutions for Kirchhoff-type diffusion problems driven by a magnetic fractional Laplacian (−Δ)As via the Galerkin method. Then, using the potential well method, we state some conditions on the initial energy, as in the case of the nonlocal Kirchhoff diffusion problem driven by fractional Laplacian, to ensure the existence of global in time solutions and blow-up in finite time solutions for our problem. The introduction of this problem could bring a new range of studies for this kind of diffusion problem.