2022/02/10 by Hui Zhan, Fei Gao, Zhan, Hui +3
Mathematics · Medicine · #26A33(secondary) #35J05(primary) #35Q92 #35R11 #92B05 #Allee effect #Analysis of PDEs (math.AP) #Applied mathematics #Demography #Diffusion #FOS: Mathematics #Fractional Differential Equations Solutions #Fractional Laplacian #G.1.8 #Laplace operator #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical physics #Mathematics #Nonlinear Differential Equations Analysis #Physics #Reaction–diffusion system #Sociology #Thermodynamics #acm:35Q92 #acm:35R11 #acm:92B05 #math.AP #msc:35Q92 #msc:35R11 #msc:92B05
paper · pdf · doi:10.48550/arxiv.2202.04928
published in arXiv (Cornell University) (Cornell University) · 35 pages, arXiv admin note: substantial text ovelap with arXiv:2112.11143
arxiv created 2022/02/10 · openalex publication_date 2022/02/10 · arxiv updated 2022/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The global boundedness and asymptotic behavior are investigated for the solutions of a nonlocal time fractional p-Laplacian reaction-diffusion equation (NTFPLRDE) \frac∂αu∂ tα=Δp u+μu2(1-kJ*u) -γu, (x,t)∈ℝN×(0,+∞) with 0<α<1,β, μ,k>0,N≤ 2 and Δpu =div(| \bigtriangledown u |p-2\bigtriangledown u). Under appropriate assumptions on J and the conditions of 1<p<2, it is proved that for any nonnegative and bounded initial conditions, the problem has a global bounded classical solution if k*=0 for N=1 or k*=(μC2GN+1)η-1 for N=2, where CGN is the constant in Gagliardo-Nirenberg inequality. With further assumptions on the initial datum, for small μ values, the solution is shown to converge to 0 exponentially or locally uniformly as t → ∞, which is referred as the Allee effect in sense of Caputo derivative. Moreover, under the condition of J ≡ 1, it is proved that the nonlinear NTFPLRDE has a global bounded solution in any dimensional space with the nonlinear p-Laplacian diffusion terms Δp um (2-(2)/(N)< m≤ 3).