Nonlinear Vibrations and the Wave Equation

Description

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. Front Matter ....Pages i-x Unbounded Linear Operators and Evolution Equations (Alain Haraux)....Pages 1-8 A Class of Abstract Wave Equations (Alain Haraux)....Pages 9-14 Almost Periodic Functions and the Abstract Wave Equation (Alain Haraux)....Pages 15-22 The Wave Equation in a Bounded Domain (Alain Haraux)....Pages 23-26 The Initial-Value Problem For A Mildly Perturbed Wave Equation (Alain Haraux)....Pages 27-33 The Initial-Value Problem in Presence of a Strong Dissipation (Alain Haraux)....Pages 35-48 Solutions on \(\mathbb {R}^{+}\) and Boundedness of the Energy (Alain Haraux)....Pages 49-54 Existence of Forced Oscillations (Alain Haraux)....Pages 55-64 Stability of Periodic or Almost Periodic Solutions (Alain Haraux)....Pages 65-71 The Conservative Case in One Spatial Dimension (Alain Haraux)....Pages 73-82 The Conservative Case in Several Spatial Dimensions (Alain Haraux)....Pages 83-90 Recent Evolutions and Perspectives (Alain Haraux)....Pages 91-98 Back Matter ....Pages 99-102