http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Global existence and large time behavior of solutions to reaction-diffusion systems with large diffusion coefficients
Systems of semilinear parabolic partial differential equations arise naturally in the modeling of certain reaction-diffusion processes. We consider m com ponent systems of the form ut = D A u + f( u ) on (r, T) x fl w ith continuous nonnegative initial d ata and homogenous Neumann boundary conditions. Here D is an m x m diagonal m atrix with positive entries on the main diagonal, f! is a sm ooth bounded domain in R n and / : R m --» R m is continuously differentiable. We show that if an a priori L1 estim ate which is independent of the diffusion coefficients and truncation is available for u and if the diffusion coefficients are sufficiently large, then the solution u exists for all time, is uniformly bounded and decays exponentially to its spatial average in L°°(fl). This work extends earlier work of Conway, Hoff and Smoller and, in addition, provides a global existence result with relatively weak assum ptions on the vector field /.