Mathematical Sciences: Integral and Integro-differential Equations in Applied Mathematics

该项目涉及一些新类型积分方程解的技术的发展，以及这些技术在各种物理问题中的应用。特别值得注意的是Volterra型方程，其解经历了爆破，以及Fredholm型方程，其解表现出边界层效应。应用领域包括(I)高强度金属中的局部塑性应变效应，(Ii)可燃固体材料的点火，以及(Iii)晶体中原子杂质的迁移。该项目涉及解决某些科学和工程问题的新技术的开发和应用，这些问题可以用数学术语表示为积分或积分-微分方程式。这些结果将被用来加强对表现出爆炸行为的现象的理解，例如固体物质的点火和燃烧。相关的应用涉及高强度金属的失效，这些金属由于极端载荷而经历粘塑性应变。另一个潜在用途涉及晶体材料中杂质的影响。

The project concerns the development of techniques for solving some new types of integral equations, and the application of these techniques to a variety of physical problems. Of particular interest are equations of Volterra type whose solution experiences a blow-up, and equations of Fredholm type whose solution exhibits boundary layer effects. The areas of application include (i) localized plastic straining effects in high-strength metals, (ii) the ignition of combustible solid materials, and (iii) the migration of atomic impurities in crystals. The project concerns the development and application of new techniques for solving certain scientific and engineering problems which can be formulated in mathematical terms as an integral or integro-differential equation. The results will be used to enhance the understanding of phenomena which exhibit explosive behavior, such as the ignition and burning of solid matter. Related applications concern the failure of high-strength metals which undergo viscoplastic strain due to extreme loading. Another area of potential use concerns the effects of impurities in crystalline materials.