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This volume will be of interest to applied mathematicians, to researchers in Partial Differential Equations, and to those involved in Fluid Dynamics and Numerical Analysis examining models for viscoelastic flows, porous medium and granular flows, and flows exhibiting phase transitions. As papers in this volume indicate, physical processes whose simplest models may involve change of type occur also in other dynamic contexts, such as in the simulation of oil reservoirs, involving multiphase flow in a porous medium, and in granular flow.