U.S.-Austria Cooperative Research on Control and Inverse Problems in Partial Differential Equations

该奖项支持南加州大学的H. T. Banks、K. Ito和C. Wang教授继续与格拉茨大学的F. Kappel教授等人以及奥地利格拉茨工业大学的K. Kunisch教授在应用数学研究方面的合作。他们在控制理论方面有共同的兴趣，集中在从已知的观察到给定过程的偏微分方程中估计参数的问题，以及强调控制和逆问题应用的泛函和偏微分方程的近似。他们将研究的具体主题包括：规模/年龄结构人口模型中的建模和参数估计技术、粘弹性系统模型中参数的可识别性、以及巴拿赫空间下非线性动力学近似框架的发展。这些美国和奥地利的数学家在开发方法和应用于函数和偏微分方程的优化、近似和参数估计等各种问题方面一直处于领先地位。他们富有成效的合作已经产生了许多出版物，其中包括对有意义的物理和生物问题的应用。提议的工作承诺通过关注与力学和人口动力学相关的技术上有趣的问题来继续这一贡献。

This award supports Professors H. T. Banks, K. Ito and C. Wang of the University of Southern California to continue their collaboration in applied mathematics research with Professor F. Kappel and others of the University of Graz and K. Kunisch of the Technical University of Graz, Austria. They share interests in control theory that focus on the problems of estimating parameters in partial differential equations from known observation of a given process and also the approximation of functional and partial differential equations stressing applications to control and inverse problems. The specific topics on which they will work include modeling and parameter estimation techniques in size/age structured population models, the identifiability of parameters in models of visco-elastic systems, and the development of an approximation framework for nonlinear dynamics in a Banach space setting. These U.S. and Austrian mathematicians have been among the leaders in the development of methods and applications in a wide variety of problems in optimization, approximation and parameter estimation for functional and partial differential equations. Their productive collaboration has already resulted in numerous publications containing applications to meaningful physical and biological problems. The proposed work promises to continue this contribution by focusing on technically interesting problems with relevance to mechanics and population dynamics.