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The research interests of Showalter include singular or degenerate nonlinear evolution equations and partial differential equations, variational inequalities and free-boundary problems, and related applications to initial-boundary-value problems of mechanics and diffusion. His current work is focused on the development of multiscale mathematical models of coupled fluid-solid dynamics, deformable porous media, and upscaled models of transport and flow in heterogeneous media. - Panta rhei