Critical parameters for reaction-diffusion equations involving space-time fractional derivatives

2018/09/19 by Sunday A. Asogwa, Mohammud Foondun, Asogwa, Sunday A. +5
Mathematics · Medicine · #35B44 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #math.AP #msc:35B44

paper · pdf · doi:10.48550/arxiv.1809.07226

arxiv created 2018/09/19 · openalex publication_date 2018/09/19 · arxiv updated 2018/09/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We will look at reaction-diffusion type equations of the following type, ∂^β_tV(t,x)=-(-Δ)^α/2 V(t,x)+I^1-β_t[V(t,x)^1+η]. We first study the equation on the whole space by making sense of it via an integral equation. Roughly speaking, we will show that when 0<η≤η_c, there is no global solution other than the trivial one while for η>η_c, non-trivial global solutions do exist. We also study the equation on a bounded domain with Dirichlet boundary condition and show that the presence of the time derivative induces a significant change in the behaviour of the solution.

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