**Fernández L.A., Mateos M., Pola C., Tröltzsch F., Zuazua E.**

Preface: A tribute to professor Eduardo Casas on his 60th birthday

Mathematical Control & Related Fields (2018, Volume 8, Issue 1) DOI: 10.3934/mcrf.201801i

**Abstract:** This special issue contains contributions to the field of Optimal Control of Partial Differential Equations submitted on the occasion of Prof. Eduardo Casas’ 60th

birthday. In total, fourteen original manuscripts are presented, covering topics in both theoretical and applied aspects and showing the state of the art in many directions of this area. These include many problems to which Eduardo Casas has made major contributions such as optimality conditions, error estimates of numerical approximations, bang-bang control, or sparse control.

Most of the contributors included here participated in the IFIP WG 7.2

Workshop ”Optimal Control of Partial Differential Equations”, held in Castro Urdiales, Spain, in September 2017. Thirty speakers from different countries (Austria, Canada, China, Ecuador, France, Germany, Greece and Spain) met together in this event in honour of Eduardo Casas. Most of them have collaborated with him at some time of his career, all of them wanting to show their appreciation and respect for his work developed along the last 35 years.

Eduardo Casas started his studies in Mathematics at Universidad Autónoma de Bilbao and completed them in 1979 at University of Zaragoza, where he got his first contract as Assistant Professor. His first indexed publication dates from 1982, the year in which he received his PhD degree under the supervision of Prof. Alfredo Bermúdez at the University of Santiago de Compostela. In 1983, Eduardo Casas moved to University of Cantabria, where he was Associate Professor until 1991, when he became Full Professor. Very soon, he formed a research group and was recognized as one of the experts of the optimal control community. An inspection in MathSciNet shows more than 130 papers, 1600 citations and 35 co-authors. Nowadays, he is Associate Editor of different scientific journals related with optimization and optimal control. This gives a rough impression of the importance and the influence of his work.

Besides his mathematical research, Eduardo Casas held some important administrative positions at the University of Cantabria in different moments of his life as Vice-President, head of the Department of Applied Mathematics and Computational Sciences, and Director of the Summer Courses. He was also President of the Spanish Society for Applied Mathematics (SeMA) and Vice-President of the Executive Committee of the International Congress of Mathematicians held in Madrid (ICM 2006).

Doing research with Eduardo Casas is a privilege. He has a broad mathematical knowledge in many topics of applied mathematics, including partial differential equations, functional analysis, numerical methods, optimization, and measure theory. He has a remarkable intuition for proving deep and new results in a very elegant way. A tireless worker, Eduardo Casas is able to convey his enthusiasm for mathematics to everyone. His research has always been timely and has set new standards in optimal control theory. We are sure that this story of success will continue for a long time.

Finally, we would like to thank the authors and reviewers for making this volume possible.

**Guest Editors:**

Luis Alberto Fernández (University of Cantabria, Spain)

Mariano Mateos (University of Oviedo, Spain)

Cecilia Pola (University of Cantabria, Spain)

Fredi Tröltzsch (Technische Universität Berlin, Germany)

Enrique Zuazua (DeustoTech – Bilbao, Basque Country & Universidad Autónoma de Madrid, Spain)

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