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Global existence and blow-up for a space and time nonlocal reaction-diffusion equation. (English) Zbl 1473.35618

Summary: A time-space fractional reaction-diffusion equation in a bounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions, solutions are global in time. Moreover, the asymptotic behavior of bounded solutions is analysed.

MSC:

35R11 Fractional partial differential equations
35B44 Blow-up in context of PDEs
35B50 Maximum principles in context of PDEs
26A33 Fractional derivatives and integrals
35K20 Initial-boundary value problems for second-order parabolic equations
35K57 Reaction-diffusion equations
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