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• W2793264757 abstract "Consider non-linear time-fractional stochastic reaction-diffusion equations of the following type, $$partial^beta_tu_t(x)=-nu(-Delta)^{alpha/2} u_t(x)+I^{1-beta}_t[b(u)+ sigma(u)stackrel{cdot}{F}(t,x)]$$ in $(d+1)$ dimensions, where $nu>0, betain (0,1)$, $alphain (0,2]$. The operator $partial^beta_t$ is the Caputo fractional derivative while $-(-Delta)^{alpha/2} $ is the generator of an isotropic $alpha$-stable Levy process and $I^{1-beta}_t$ is the Riesz fractional integral operator. The forcing noise denoted by $stackrel{cdot}{F}(t,x)$ 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 $b$, $sigma$ and the initial condition. Our results complement those of P. Chow in cite{chow2}, cite{chow1}, and Foondun et al. in cite{Foondun-liu-nane}, cite{foondun-parshad} among others." @default.
• W2793264757 created "2018-03-29" @default.
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• W2793264757 date "2018-03-15" @default.
• W2793264757 modified "2023-09-27" @default.
• W2793264757 title "Blow-up results for space-time fractional stochastic partial differential equations" @default.
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