Blow-Up Results for Space-Time Fractional Stochastic Partial Differential Equations View Full Text


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Article Info

DATE

2019-03-07

AUTHORS

Sunday A. Asogwa, Jebessa B. Mijena, Erkan Nane

ABSTRACT

Consider non-linear time-fractional stochastic reaction-diffusion equations of the following type, ∂tβut(x)=−ν(−Δ)α/2ut(x)+I1−β[b(u)+σ(u)F⋅(t,x)] in (d + 1) dimensions, where ν > 0,β ∈ (0, 1), α ∈ (0, 2]. The operator ∂tβ is the Caputo fractional derivative while − (−Δ)α/2 is the generator of an isotropic α-stable Lévy process and I1−β is the Riesz fractional integral operator. The forcing noise denoted by F⋅(t,x) is a Gaussian noise. These equations might be used as a model for materials with random thermal memory. We derive non-existence (blow-up) of global random field solutions under some additional conditions, most notably on b, σ and the initial condition. Our results complement those of P. Chow in (Commun. Stoch. Anal. 3(2):211–222, 2009), Chow (J. Differential Equations 250(5):2567–2580, 2011), and Foondun et al. in (2016), Foondun and Parshad (Proc. Amer. Math. Soc. 143(9):4085–4094, 2015) among others. More... »

PAGES

1-30

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http://scigraph.springernature.com/pub.10.1007/s11118-019-09772-0

DOI

http://dx.doi.org/10.1007/s11118-019-09772-0

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