Contemporary PDEs between theory and applications

This special issue of Discrete and Continuous Dynamical Systems is devoted to some recent developments in some important fields of partial differential equations. The aim is to bring together several contributions in different fields that range from classical to modern topics with the intent to present new research perspectives, innovative methods and challenging applications. Though it was of course impossible to take into account all the possible lines of research in PDEs, we tried to present a wide spectrum, hoping to capture the interest of both the general mathematical audience and the specialized mathematicians that work in differential equations and related fields. We think that the Authors put a great effort to write their contributions in the clearest possible language. We are indeed grateful to all the Authors that contributed to this special issue, donating beautiful pieces of mathematics to the community and promoting further developments in the field. We also thank the Managing Editor for his kind invitation to act as an editor of this special issue. Also, we express our gratitude to all the Referees who kindly agreed to devote their time and efforts to read and check all the papers carefully, providing useful comments and recommendations. Indeed, each paper was submitted to the meticulous inspection of two independent and anonymous Experts, whose observations were fundamental to the final outcome of this special issue. Finally, we would like to wish a `Happy reading!' to the Reader. This volume is for Her (or Him), after all.