2023/11/26 by Guy Foghem, Foghem, Guy, David Padilla‐Garza +3
Computer Science · Mathematics · #35A15 #35R09 #35R11 #35S10 #46E35 #47A07 #49J40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2311.15340
openalex publication_date 2023/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a porous medium-type equation whose pressure is given by a nonlocal Lévy operator associated to a symmetric jump Lévy kernel. The class of nonlocal operators under consideration appears as a generalization of the classical fractional Laplace operator. For the class of Lévy-operators, we construct weak solutions using a variational minimizing movement scheme. The lack of interpolation techniques is ensued by technical challenges that render our setting more challenging than the one known for fractional operators.