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Positivity and explosion in mean Lp-norm of stochastic functional parabolic equations of retarded type

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  • Chow, Pao-Liu
  • Liu, Kai
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    Abstract

    This work is concerned with a class of semilinear stochastic functional parabolic differential equations of retarded type. We first establish conditions to ensure the existence of a unique non-negative solution of the stochastic delay partial differential equation under investigation. Subsequently, the problem of explosive or blow-up solutions in mean Lp-norm sense, p≥1, in a finite time to the stochastic system is considered. Several examples are given to illustrate the theory established in the work.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 4 ()
    Pages: 1709-1729

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1709-1729

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    Related research

    Keywords: Positivity of solutions; Blow-up of solutions in mean Lp-norm; Stochastic functional reaction–diffusion equations of retarded type;

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