Explosive behavior in spatially discrete reaction-diffusion systems

Ana Carpio; Gema Duro

doi:10.3934/dcdsb.2009.12.693

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2009, Volume 12, Issue 4: 693-711. Doi: 10.3934/dcdsb.2009.12.693

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Explosive behavior in spatially discrete reaction-diffusion systems

Ana Carpio^1, and
Gema Duro^2,

1.
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040
2.
Departamento de Análisis Económico: Economía Cuantitativa, Universidad Autónoma de Madrid, Madrid 28049

Received: March 2008

Revised: May 2009

Published: November 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 65P40, 65J20; Secondary: 65N40.

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