Global existence and blow-up of solutions for a parabolic equation involving the fractional p(x)-Laplacian

2020/06/21 by Boudjeriou, Tahir
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.11859

Abstract

In this paper, we consider a non-local diffusion equation involving the fractional p(x)-Laplacian with nonlinearities of variable exponent type. Employing the sub-differential approach we establish the existence of local solutions. By combining the potential well theory with the Nehari manifold, we obtain the existence of global solutions and finite time blow-up of solutions. Moreover, we study the asymptotic stability of global solutions as time goes to infinity in some variable exponent Lebesgue spaces.

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