2015/07/16 by Félix del Teso, del Teso, Félix, Jørgen Endal +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1507.04659
openalex publication_date 2015/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study the uniqueness, existence, and properties of bounded distributional\nsolutions of the initial value problem problem for the anomalous diffusion\nequation \∂tu-\L^\μ [\φ (u)]=0. Here \L^\μ\ncan be any nonlocal symmetric degenerate elliptic operator including the\nfractional Laplacian and numerical discretizations of this operator. The\nfunction \φ:\ℝ \→ \ℝ is only assumed to be continuous\nand nondecreasing. The class of equations include nonlocal (generalized) porous\nmedium equations, fast diffusion equations, and Stefan problems. In addition to\nvery general uniqueness and existence results, we obtain L1-contraction and\na priori estimates. We also study local limits, continuous dependence, and\nproperties and convergence of a numerical approximation of our equations.\n