Existence of weak solutions to a continuity equation with space time\n nonlocal Darcy law

2018/05/22 by Luis Caffarelli, Caffarelli, Luis, Maria Pia Gualdani +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1805.08666

openalex publication_date 2018/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this manuscript we consider a porous medium equation with non-local\ndiffusion effects given by a fractional heat operator \∂_t +\n(-\Δ)^s in two space dimensions. Global in time existence of weak\nsolutions is shown by employing a time semi-discretization of the equations, an\nenergy inequality, a higher order integral estimate, and a generalized version\nof the Div-Curl lemma.\n

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