A Neumann problem for a diffusion equation with n-dimensional fractional Laplacian

Advances in Difference Equations

Francisco J. Ariza-Hernandez¹  Jorge Sanchez-Ortiz¹  Eduard Garcia-Murcia¹  Martin P. Arciga-Alejandre¹ 

[1] Facultad de Matemáticas, Universidad Autónoma de Guerrero;

关键词: Fractional Laplacian;    Fokas method;    Green function;   

DOI  :  10.1186/s13662-021-03413-w

来源: DOAJ

【 摘 要 】

Abstract We study an initial-boundary value problem for a n-dimensional stochastic diffusion equation with fractional Laplacian on R + n $\mathbb{R}_{+}^{n}$ . In order to prove existence and uniqueness, we generalize the Fokas method to construct the Green function for the associated linear problem and then we apply a fixed point argument. Also, we present an example where the explicit solutions are given.

【 授权许可】

Unknown