Mathematical analysis of a model for nuclear reactor dynamics
type: Item
instance of: scholarly article
title: Mathematical analysis of a model for nuclear reactor dynamics
zbMATH Open document ID: 0810.45004
author: Ziqian Yan
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-04-10T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45F05
Mathematics Subject Classification ID: 82D75
zbMATH DE Number: 703294
zbMATH Keywords: existence
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: blowing-up property
zbMATH Keywords: nonlinear integro- differential reaction-diffusion system
zbMATH Keywords: nuclear reactor dynamics
zbMATH Keywords: unique global solution
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1322
OpenAlex ID: W2008979021
DOI: 10.1006/JMAA.1994.1322
description: scientific article; zbMATH DE number 703294