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Explosive behavior in spatially discrete reaction-diffusion systems

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  • Explosive instabilities in spatially discrete reaction-diffusion systems are studied. We identify classes of initial data developing singularities in finite time and obtain predictions of the blow-up times, whose accuracy is checked by comparison with numerical solutions. We present averaged and local blow-up estimates. Local blow-up results show that it is possible to have blow-up after blow-up. Conditions excluding or implying blow-up at space infinity are discussed.
    Mathematics Subject Classification: Primary: 65P40, 65J20; Secondary: 65N40.


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