Exact Controllability and Stabilization of the Wave Equation

Abstract

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, were initially published in 1989 in Spanish under the title "Controlabilidad Exacta y Estabilizaci\'on de la Ecuaci\'on de Ondas" in the Lecture Notes Series of the Institute. 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 Universit\'e Pierre et Marie Curie in Paris and drafting the lectures of Professor Jacques-Louis Lions at Coll\`ege 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 during my PhD under the supervision of Professor Alain Haraux in Paris.