Mathematical Sciences: Studies in Continuum Mechanics and Partial Differential Equations

本研究项目是研究非线性偏微分方程解和积分方程解的定性特征，这两个方程是力学和生物学中许多应用领域的数学模型。在广泛的力学领域内，该研究计划特别关注可混相可压缩气体在多孔介质中的流动，相界面的平衡问题，混合物理论和非线性粘弹性。在生物学领域，该研究计划特别关注相互作用的种群的扩散、老年结构种群的动态和肌肉收缩。

This research program is a study of qualitative features of the solutions of nonlinear partial differential equations and integral equations which are mathematical models of a number of application areas in mechanics and biology. Within the broad area of mechanics, the research program focuses specifically on flows of miscible compressible gases in porous media, equilibrium problems of phase interfaces, mixture theory and nonlinear viscoelasticity. In the area of biology, the research program focuses specifically on the dispersal of interacting populations, the dynamics of aged-structured population and muscular contraction.