The research interests of Showalter include singular or degenerate nonlinear evolution equations and partial differential equations, related variational inequalities and free-boundary problems, and 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. He is a member of the Multiscale Mathematics Research Group and the Northwest Consortium in Multiscale Mathematics.