Volume 43_2_(2022)_103-132

On the behavior of entropy solutions for a fractional p-Laplacian problem as t tends to infinity
Mohammed Abdellaoui

Abstract. The paper studies the mixed Dirichlet-Cauchy problem for a fractional parabolic equation on a bounded domain. The elliptic part of the operator is a fractional p-Laplacian, a forcing term is allowed, which is a nonnegative finite Radon measure, while the initial datum is a nonnegative L1 function. The main result concerns the asymptotic behavior of entropy solutions and it is proved that the solutions of the parabolic problem converge, in the L1 sense, to a solution of the corresponding stationary problem both in the homogeneous and in the nonhomogeneous case

Rend. Mat. Appl. (7) 43 (2022) 103-132;  pdf