Nonlinear Vibrations and the Wave Equation (eBook)
X, 102 Seiten
Springer International Publishing (Verlag)
978-3-319-78515-8 (ISBN)
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.
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.
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.
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.
| Erscheint lt. Verlag | 2.5.2018 |
|---|---|
| Reihe/Serie | SpringerBriefs in Mathematics | SpringerBriefs in Mathematics |
| Zusatzinfo | X, 102 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Schlagworte | Almost periodic oscillations • Damped equation with source term • Functional Analysis • Nonlinear Vibrations • Partial differential equations • wave equation |
| ISBN-10 | 3-319-78515-X / 331978515X |
| ISBN-13 | 978-3-319-78515-8 / 9783319785158 |
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