BLOWUP IN A PARTIAL-DIFFERENTIAL EQUATION WITH CONSERVED 1ST INTEGRAL

A reaction-diffusion equation with a nonlocal term is studied. The non local term acts to conserve the spatial integral of the unknown functi on as time evolves. Such equations give insight into biological and ch emical problems where conservation properties predominate. The aim of the paper is to understand how the conservation property affects the n ature of blowup. The equation studied has a trivial steady solution th at is proved to be stable. Existence of nontrivial steady solutions is proved, and their instability established numerically. Blowup is prov ed for sufficiently large initial data by using a comparison principle in Fourier space. The nature of the blowup is investigated by a combi nation of asymptotic and numerical calculations.