一类核反应堆数学模型正解的全局分歧

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一类核反应堆数学模型正解的全局分歧陈瑞鹏, 李小亚北方民族大学数学与信息科学学院, 银川 750021 Global Bifurcation of Positive Solutions of a Mathematical Model Arising In Nuclear Engineering CHEN Ruipeng, LI XiaoyaCollege of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China

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摘要本文研究一类源于核反应堆的数学模型正解的存在性.该模型旨在描述与快中子流密度、反应堆温度紧密相关的核反应过程.本文主要讨论反应堆与外界有热交换的情形.从数学的角度来看，模型自身的非合作特性导致对正解存在性及相关性质的研究较为困难，适用于研究合作系统的比较原理等方法将不再有效.运用分歧理论，我们获得了该模型存在正解的充分必要条件，建立了正解的全局分歧结果，同时对正解的渐近行为进行了仔细分析.所得结果丰富并补充了核反应堆数学模型的相关理论.

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收稿日期: 2017-07-12

PACS:

O175.8

基金资助:国家自然科学基金（61761002，11601011），北方民族大学校级科研一般项目（2018XYZSX03）和北方民族大学重大专项项目经费（ZDZX201804）资助项目.

引用本文:

陈瑞鹏, 李小亚. 一类核反应堆数学模型正解的全局分歧[J]. 应用数学学报, 2018, 41(5): 596-608. CHEN Ruipeng, LI Xiaoya. Global Bifurcation of Positive Solutions of a Mathematical Model Arising In Nuclear Engineering. Acta Mathematicae Applicatae Sinica, 2018, 41(5): 596-608.

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