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

Asogwa, Sunday A. and Foondun, Mohammud and Mijena, Jebessa B. and Nane, Erkan (2020) Critical parameters for reaction-diffusion equations involving space-time fractional derivatives. Nonlinear Differential Equations and Applications NoDEA, 27 (3). 30. ISSN 1420-9004 (https://doi.org/10.1007/s00030-020-00629-9)

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Abstract

We will look at reaction–diffusion type equations of the following type, ∂tβV(t,x)=-(-Δ)α/2V(t,x)+It1-β[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. The critical parameter η c is shown to be 1η∗ where η∗:=supa>0{supt∈(0,∞),x∈Rdta∫RdG(t,x-y)V0(y)dy<∞}and G(t,x) is the heat kernel of the corresponding unforced operator. V is a non-negative initial function. We also study the equation on a bounded domain with Dirichlet boundary condition and show that the presence of the fractional time derivative induces a significant change in the behavior of the solution.

  • Item type:Article
    ID code:72342
    Dates:
    Date
    Event
    30 June 2020
    Published
    6 May 2020
    Published Online
    14 March 2020
    Accepted
    19 September 2018
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:13 May 2020 11:08
    Last modified:09 Apr 2024 00:18
    URI:https://strathprints.strath.ac.uk/id/eprint/72342
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