This article is cited in 22 papers

Reaction versus diffusion: blow-up induced and inhibited by diffusivity

M. Fila^a, H. Ninomiya<sup>b

a</sup> Comenius University
^b Ryukoku University

Abstract: 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.

UDC: 517.947

MSC: Primary 35K57, 35B35; Secondary 34D23, 35A05, 35B41, 34D45

Received: 02.10.2005

DOI: 10.4213/rm1684

 English version: Russian Mathematical Surveys, 2005, 60:6, 1217–1235

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