Existence and global behaviour of solutions of a parabolic problem involving the fractional p -Laplacian in porous medium
Year: 2025
Type: article
Abstract: In this paper, we prove the existence and the uniqueness of a weak and mild solution of the following nonlinear parabolic problem involving the porous $p$-fractional Laplacian: \begin{equation*} \begin{cases} \partial_t u+(-Δ)^s_p(|u|^{m-1}u)=h(t,x,|u|^{m-1}u) & \text{in} \; (0,T)\times Ω,\\ u=0 & \text{in} \; (0,T) \times \mathbb{R}^d\backslash Ω, \\ u(0,\cdot)=u_0 & \text{in} \; Ω. \end{cases}\ \end{equation*} We also study further the the homogeneous case $h(u)=|u|^{q-1}u$ with $q>0$. In particular we investigate global time existence, uniqueness, global behaviour of weak solutions and stabilization.
Authors: Loïc Constantin, Jacques Giacomoni, Guillaume Warnault
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,780
OpenAlex ID: W4410856151