دانلود کتاب کنترل‌پذیری دقیق و پایدارسازی معادله موج

These Notes originated from a course I delivered at the Institute of Mathematics of the Universidade Federal do Rio de Janeiro, Brazil (UFRJ), in July-September 1989. I had the honor of visiting this institution upon the invitation and hospitality of Prof. Carlos Frederico Vasconcellos, affectionately known as Fred to his colleagues and friends. The dynamic and friendly team led by Prof. Luiz Adauto Medeiros warmly welcomed me. These Notes were initially published in 1989 in Spanish under the title “Contro-labilidad Exacta y Estabilización de la Ecuación de Ondas” in the Lecture Notes Series of the Institute. Spanish and Portuguese are sister languages and we believed that mathematicians at the Institute and in Brazil, as well as Portuguese speakers more broadly, could read and use them without language barriers. I am indebted to Fred, who, with this invitation in 1989, opened up numerous opportunities for me early in my career. This experience allowed me to learn about Brazil and become fascinated by the country, its culture, nature, and people. I can never thank him enough. My gratitude extends to the entire Brazilian mathematical community, which has offered and continues to offer abundant opportunities for foreign mathematicians and has witnessed remarkable qualitative and quantitative growth over the last three decades. Francesca Bonadei, whom with I had the pleasure and honor to cooperate in a number of publishing and editorial efforts in the Mathematical Sciences during the last12years, recently invitedmetotranslatetheseNotes intoEnglishforpublication by Springer Nature in the UNITEXT book series, whose editorial board led by Alfio Quarteroni was kind enough to support the publication. Despite the significant evolution of the topic over the last three decades, I believe that the text, with its synthetic presentation of fundamental tools in the field, remains valuable for researchers in the area, especially for younger generations. It is written from the perspective of the young mathematician I was when I authored the Notes, needing to learn many things in the process and, therefore, taking care to develop details often left to the reader or not readily available elsewhere. These Notes were written one year after completing my PhD at the Université Pierre et Marie Curie in Paris and drafting the lectures of Professor Jacques-Louis Lions at Collège de France in the academic year 1986–1987, later published as a book in 1988. Parts of these Notes offer a concise presentation of content developed in more detail in that book, supplemented by work on the decay of dissipative wave equations carried out during my PhD under the supervision of Professor Alain Haraux in Paris. I cannot conclude without extending my warmest thanks to Alain Haraux and Jacques-Louis Lions, whose significant, generous, and positive influence has greatly impacted my career and life.