Numerical analysis of finite-time blow-up in nonlinear integro-differential equations

非线性积分微分方程有限时间爆炸的数值分析

• 批准号: 9406-2011
• 负责人: Brunner, Hermann
• 金额: $ 0.95万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508545
• 关键词: Numerical; analysis; finite; time; blow

Nonlinear integral equations of Volterra type arise in the mathematical modelling of thermal ignition in solid combustible materials (e.g. in the formation of shear bands in steel, when subjected to very high strain rates; see the review paper by C.A. Roberts in J. Comput. Appl. Math 205 (2007), 736-743, and its references). Such equations -- whose solutions blow up in finite time -- are also related to semilinear parabolic partial differential equations of reaction-diffusion type; compare the book 'Mathematical Problems from Combustion Theory' (1989) by J. Bebernes and D. Eberly, and the review paper by H.A. Levine in SIAM Review 32 (1990), 262-288.

沃尔泰拉类型的非线性积分方程出现在固体可燃材料的热点燃的数学模型中（例如，当受到非常高的应变率时，在钢中形成剪切带;见C.A.罗伯茨在J. Comput。Math 205（2007），736-743及其参考文献）。这样的方程--其解在有限时间内爆破--也与反应扩散型的半线性抛物偏微分方程有关;比较J. Bebernes和D. Eberly和H.A. Levine in SIAM Review 32（1990），262-288.