| Abstract: |
| We consider a flow problem in heterogeneous porous media with strongly varying properties. Such situations naturally arise in practical applications, particularly in petroleum reservoir engineering and groundwater flow, where abrupt changes in the medium induce discontinuous coefficients.
This motivates the study of a nonlocal diffusion model involving a fractional gradient operator with a spatially varying and discontinuous coefficient $\beta(x) \geq \beta_* > 0$, capturing multiscale effects and anomalous transport phenomena.
We construct a family of approximating problems by combining a regularizing diffusion term with a suitable approximation procedure. The analysis is carried out in an appropriate functional framework for weak solutions. We establish existence, positivity, and continuous dependence on the data, and derive uniform a priori estimates. These estimates allow us to pass to the limit in the approximating problems and obtain a solution to the limiting problem.
This is joint work with Eduardo Abreu, Assis Azevedo, Julio Guevara, and Lisa Santos. |
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