Nonlinear Vibrations and the Wave Equation

Prof. Alain Haraux studied at the Ecole Normale Superieure, Paris from 1969 to 1973. He became a researcher at the CNRS, France in 1973 and received his HDR (habilitation to conduct research) in Mathematics from the University of Paris 6 (now: Sorbonne University) in 1978. He is currently an Emeritus Director of Research at the CNRS, and is the author of more than 150 specialized papers and 6 books. Throughout his career, his main field of research has been the long-term behavior of the solutions to nonlinear partial differential equations, in particular such topics as stability, near-periodicity, oscillation theory, maximal attractors, stabilization theory and exact controllability.

“The text is written in a lucid and reader-friendly style, and it requires only a basic knowledge of functional analysis to be understood. … This nice monograph is recommended to everybody interested in a concise but clear introduction to dissipative wave equations in bounded domains. It leads the reader to understand open problems in a classical research area which is still far from being completely explored.” (Enzo Vitillaro, Mathematical Reviews, December, 2018)

• 1 Unbounded Linear Operators and Evolution Equations.- 2 A Class of Abstract Wave Equations.- 3 Almost Periodic Functions and the Abstract Wave Equation.- 4 The Wave Equation in a Bounded Domain.- 5 The Initial-Value Problem for a Mildly Perturbed Wave Equation.- 6 The Initial-Value Problem in Presence of a Strong Dissipation.- 7 Solutions on R+ and Boundedness of the Energy.- 8 Existence of Forced Oscillations.- 9 Stability of Periodic or Almost Periodic Solutions.- 10 The Conservative Case in One Spatial Dimension.- 11 The Conservative Case in Several Spatial Dimensions.- 12 Thirthy Years After.