U.S.-Chile Collaboration: Some Parabolic Equations and Systems of Ordinary Differential Equations with p-Laplacian Type of Operators

0204032沃德这是阿拉巴马大学伯明翰分校的詹姆斯·R·沃德博士、智利大学的劳尔·马纳塞维奇博士和玛尔塔·加西亚·惠多布罗博士分别与智利大学和智利卡托利卡大学的合作研究项目。研究人员打算从事偏微分方程边值问题的数学分析。这些问题既出现在慢扩散模型中，也出现在快速扩散模型中，并且在人口和疾病、多孔介质以及固有的非线性问题的研究中很有用。研究人员将使用拓扑工具，例如次数和同伦指数，它们是系统行为的有用指标。每一方都有自己的长处：Garcia-Huidobro博士和Manasevich博士在拟线性微分方程和分叉方面拥有丰富的经验，而Ward博士在他们的共同努力中使用了大量的拓扑工具。

0204032WardThis is a collaborative research project between Dr. James R. Ward of University of Alabama at Birmingham, and Dr. Raul Manasevich and Marta Garcia-Huidobro of Universidad de Chile and Pontifica Universidad Catolica de Chile respectively. The investigators intend to work on the mathematical analysis of boundary value problems for partial differential equations. These problems appear in modeling both slow and fast diffusion, and are useful in the study of populations and diseases, porous media, and problems that are inherently nonlinear. The investigators will use topological tools, such as degree and homotopy indexes, that are useful indicators of system behavior.Each side brings their own strengths to the collaboration: Drs. Garcia-Huidobro and Manasevich have extensive experience in quasilinear differential equations and bifurcations, while Dr. Ward has worked at length with the topological tools to be used in their joint effort.