Calculus of Variations and Geometric Measure Theory

G. Franzina - B. Volzone

Large time behavior of fractional porous media equation

created by franzina on 08 Feb 2023
modified on 04 Jun 2024


Published Paper

Inserted: 8 feb 2023
Last Updated: 4 jun 2024

Journal: Journal of Evolution Equations
Year: 2023
Doi: 10.1007/s00028-023-00920-z


Following the methodology of Brasco and Volzone, Adv. Math. 2022, we study the long-time behavior for the signed Fractional Porous Medium Equation in open bounded sets with smooth boundary. Homogeneous exterior Dirichlet boundary conditions are considered. We prove that if the initial datum has sufficiently small energy, then the solution, once suitably rescaled, converges to a nontrivial constant sign solution of a sublinear fractional Lane-Emden equation. Furthermore, we give a nonlocal sufficient energetic criterion on the initial datum, which is important to identify the exact limit profile, namely the positive solution or the negative one.