Data for "Stability of saltwater-freshwater mixing zones in beach aquifers with geologic heterogeneity"
This resource contains example model input and output data for Olorunsaye and Heiss (2024). Olorunsaye, O., & Heiss, J. W. (2024). Stability of saltwater‐freshwater mixing zones in beach aquifers with geologic heterogeneity. Water Resources Research, e2023WR036394, 1–22. https://doi.org/10.1029/2023WR036056
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- PAR ID:
- 10594051
- Publisher / Repository:
- HydroShare
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We extend the Calderón–Zygmund theory for nonlocal equations tostrongly coupled system of linear nonlocal equations {\mathcal{L}^{s}_{A}u=f}, where the operator {\mathcal{L}^{s}_{A}}is formally given by \mathcal{L}^{s}_{A}u=\int_{\mathbb{R}^{n}}\frac{A(x,y)}{|x-y|^{n+2s}}\frac{(x-%y)\otimes(x-y)}{|x-y|^{2}}(u(x)-u(y))\,dy. For {0more » « less
<1}and {A:\mathbb{R}^{n}\times\mathbb{R}^{n}\to\mathbb{R}}taken to be symmetric and serving asa variable coefficient for the operator, the system under consideration is the fractional version of the classical Navier–Lamé linearized elasticity system. The study of the coupled system of nonlocal equations is motivated by its appearance in nonlocal mechanics, primarily in peridynamics. Our regularity result states that if {A(\,\cdot\,,y)}is uniformly Holder continuous and {\inf_{x\in\mathbb{R}^{n}}A(x,x)>0}, then for {f\in L^{p}_{\rm loc}}, for {p\geq 2}, the solution vector {u\in H^{2s-\delta,p}_{\rm loc}}for some {\delta\in(0,s)}.
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