Geodesic
Reaction versus diffusion: blow-up induced and inhibited by diffusivity
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 6, pp. 1217-1235

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A survey is given of results on the relation of the dynamics of a system of ordinary differential equations to the dynamics of the corresponding reaction-diffusion system when diffusion is added. The main interest here is in the influence of diffusion on the global existence of solutions. Examples are presented of systems where diffusion induces or inhibits blow-up. 
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     title = {Reaction versus diffusion: blow-up induced and inhibited by diffusivity},
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M. Fila; H. Ninomiya. Reaction versus diffusion: blow-up induced and inhibited by diffusivity. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 6, pp. 1217-1235. http://geodesic.mathdoc.fr/item/RM_2005_60_6_a12/