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November  2009, 12(4): 693-711. doi: 10.3934/dcdsb.2009.12.693

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, Spain
2. 

Departamento de Análisis Económico: Economía Cuantitativa, Universidad Autónoma de Madrid, Madrid 28049, Spain

Received  March 2008 Revised  May 2009 Published  August 2009

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.
Keywords: reaction-diffusion systems, Instability, nonlinear oscillators., spatial discreteness, blow-up.
Mathematics Subject Classification: Primary: 65P40, 65J20; Secondary: 65N4.
Citation: Ana Carpio, Gema Duro. Explosive behavior in spatially discrete reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 693-711. doi: 10.3934/dcdsb.2009.12.693
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