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This volume gathers contributions in the field of Partial Differential Equations, with particular emphasis to mathematical models in Phase Transitions, Complex Fluids, Thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. In particular, the following thematic areas are developed: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner; as a general strategy, the articles describe some new achievements and/or the state of the art in their line of research, providing to the interested readers an overview of recent progress and future research items in PDEs.