Mathematical analysis of a model for nuclear reactor dynamics (Q1340510)

The author studies the global existence, asymptotic behavior and blowing- up property of the following nonlinear integro-differential reaction- diffusion system \(u_ t + Lu = \lambda u + \mu u \int^ t_ 0 u(x,s)ds\), \(Bu = 0\), \(u(x,0) = u_ 0(x)\), where \(L\) is a uniformly elliptic, self-adjoint operator, which arises in nuclear reactor dynamics: \(Lu = - \sum^ n_{i,j=1} {\partial \over \partial x_ i} (a_{ij} (x) {\partial u \over \partial x_ j}) + a_ 0 (x)u\), \(Bu = a(x) {\partial u \over \partial \gamma} + \beta (x)u\), where \(a_{ij} (x)\), \(a_ 0 (x)\), \(a(x)\) and \(\beta (x)\) are suitably smooth functions, and \(u_ 0 (x)\) is a bounded nonnegative continuous function. Two main results are proved for the unique global solution of the problem.