This book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro in 1986, then in Tokyo in 1987. An additional chapter has been added to reflect more recent advances in the field.
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.
"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)