Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport

Technical Report · Mon Jan 11 23:00:00 EST 2021

DOI:https://doi.org/10.2172/1763574· OSTI ID:1763574

D'Elia, Marta ^[1]; Gulian, Mamikon ^[1]

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1. Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)

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.

• Research Organization: Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• DOE Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1763574
• Report Number(s): SAND--2021-0098R; 693201
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
anisotropic diffusion
anomalous diffusion
fractional models
nonlocal models
solute transport