Nonlinear Vibrations and the Wave Equation
1st Edition
Published on 2. May 2018
X, 102 pages
978-3-319-78515-8 (ISBN)
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.
Reviews / Votes
"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)More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Primary & secondary/elementary & high school
Product notice
Reflowable
Illustrations
X, 102 p.
File size
1,82 MB
ISBN-13
978-3-319-78515-8 (9783319785158)
DOI
10.1007/978-3-319-78515-8
Schweitzer Classification
Other editions
Additional editions
Alain Haraux
Nonlinear Vibrations and the Wave Equation
Book
05/2018
Springer
€53.49
Shipment within 10-15 days
Person
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.
Content
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.
