TY - JOUR
T1 - Analysis of Anisotropic Nonlocal Diffusion Models: Well-Posedness of Fractional Problems for Anomalous Transport
AU - D’Elia , Marta
AU - Gulian , Mamikon
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 851
EP - 875
PY - 2022
DA - 2022/10
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2022-0001s
UR - https://global-sci.org/intro/article_detail/nmtma/21083.html
KW - Nonlocal models, fractional models, anomalous diffusion, anisotropic diffusion, solute transport.
AB - <p style="text-align: justify;">We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic
nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection
equation and prove well-posedness for fractional orders $s ∈ [0.5, 1).$ We also present
an application of the advection-diffusion equation to anomalous transport of solutes.</p>