Mathematical Sciences: Homogenization and Oscillation Effects in Some Systems of Partial Differential Equations ofContinuum Mechanics

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The goal of this project is to study the applications to continuum mechanics of a mathematical tool developed by the principal investigator. This tool, called H theory, is an outgrowth of homogenization theory, which was also developed largely by the principal investigator. Particular areas to be studied include effective properties of mixtures, non-local effects induced by homogenization, long-time behavior of fluid interfaces, evolution of the microstructure of composite materials and nonlinear vibrations of solids.