U.S.-Austria Cooperative Research: Volterra Integral Equations and Applications

该奖项将支持为期两年的合作研究工作， 数学涉及教授罗纳德C.格里默 卡本代尔大学教授。米勒，爱荷华州 奥地利格拉兹大学Wilhelm Schappacher教授; 以及同样来自格拉兹大学的沃尔夫冈·德施博士。 的 合作的数学家们正在研究一些相关的问题 涉及所谓的沃尔泰拉积分微分方程 空间 他们的研究将涉及各种问题， 偏微分方程解的控制与定性 积分方程 特别感兴趣的是确定 解的行为，在初始或 边界数据 重要的是要确定这些奇点 传播，如果是这样，另外确定这些行为 奇点 也将包括渐近行为的研究 特别是当它与控制问题有关时。 这项研究的预期结果在很大程度上是抽象的 数学性质，但这项工作很可能导致数学 适用于实际问题的技术，例如 在研究既具有粘性又具有粘性的材料的物理行为时， 和弹性。 这种粘弹性介质的实例是 聚合物固体、高分子量聚合物流体、血液，以及 流化煤 所研究方程的另一个应用 为电动力学干杯。 数学家们合作研究 项目具有相似和互补的优势和利益。 他们在过去一起工作富有成效，这个奖项将 让他们继续进行互利合作。

This award will support a two-year collaborative research effort in mathematics involving Professor Ronald C. Grimmer, Southern Illinois University at Carbondale; Professor Richard K. Miller, Iowa State University; Professor Wilhelm Schappacher, University of Graz, Austria; and Dr. Wolfgang Desch, also at the University of Graz. The cooperating mathematicians are studying a number of related problems involving so-called Volterra integrodifferential equations in Banach space. Their research will deal with various questions concerning control and qualitative behavior of solutions of partial differential integral equations. Of particular interest will be determining the behavior of solutions which have singularities in the initial or boundary data. It is important to determine if these singularities propagate and, if so, additionally to determine the behavior of these singularities. Included also will be the study of asymptotic behavior of solutions especially as it is related to control problems. The expected results of this research will be largely of an abstract mathematical nature, but the work may well lead to mathematical techniques which are applicable to practical problems, as for example in the study of the physical behavior of materials having both viscous and elastic properties. Examples of such viscoelastic media are polymeric solids, high molecular weight polymer fluids, blood, and fluidized coal. Another application of the equations being studied here is to electrodynamics. The mathematicians collaborating in this project have both similar and complementary strengths and interests. They have worked together productively in the past, and this award will permit them to continue their mutually beneficial cooperation.