Logistic elliptic and parabolic problem for the fractional p-Laplacian

2025/11/28 by Loïc Constantin, Carlos Alberto Santos, Constantin, Loïc +3
Mathematics · #Differential Equations and Boundary Problems #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.2511.23272

openalex publication_date 2025/11/28 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

In this paper we prove existence, uniqueness of weak solutions of the following nonlocal nonlinear logistic equation \begincases (-Δ)_p^s u_λ=λu_λ^q - b(x)u_λ^r in Ω,
u_λ=0 in ( ℝ^d \backslash Ω),
u_λgt;0 in Ω. \endcases We also prove behavior of u_λ with respect to λ, underlining the effect of the nonlocal operator. We then study the associated parabolic problem, proving local and global existence, uniqueness and global behavior such as stabilization, finite time extinction and blow up.

Citations

• Reformulation of elasticity theory for discontinuities and long-range forces

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