Mathematical Sciences: Studies in Continuum Mechanics and Partial Differential Equations

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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.