Inverse problems in partial differential equations

偏微分方程中的反问题

• 批准号: 250240-2010
• 负责人: Nachman, Adrian
• 金额: $ 2.19万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=455622
• 关键词: Inverse; problems; partial; differential; equations

When scientists and engineers seek to determine properties of the interior of an object (e.g. the human body, the nucleus of an atom, an airplane wing, the earth, or the sun) without penetrating or even accessing the object, the analyze its effect on acoustic, elastic, electromagnetic or quantum mechanical waves. Mathematically, wave propagation is modeled by Partial Differential Equations and the class of problems considered in the proposed research consists in determining the coefficients of such and equation (which encode the unknown medium properties) from available measurements of the solutions (the waves).

当科学家和工程师试图在不穿透甚至接触物体的情况下确定物体(例如，人体、原子核、飞机机翼、地球或太阳)内部的特性时，科学家和工程师可以分析其对声波、弹性波、电磁波或量子力学波的影响。在数学上，波的传播由偏微分方程组来模拟，所考虑的问题包括根据解(波)的可用测量来确定此类和方程(编码未知介质属性)的系数。