Exponential Stability for the Damped Wave Equation

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Outline:

Contents
1 Introduction
2 Background Material
3 Statement of the problem
3.1 Geometrical conditions
3.2 Well-posedness
3.3 Some stability tools
4 Case of the linear damped wave equation
4.1 Case of a globally distributed damping with unitary damping coefficient
4.1.1 An equivalent norm
4.1.2 Exponential stability
4.2 Case of a locally distributed damping
4.2.1 Case of one observation point
4.2.2 One dimensional case
5 Case of the nonlinear damped wave equation
5.1 Case of a globally distributed damping with unitary damping coefficient
5.1.1 Exponential stability
5.2 Case of a locally distributed damping
6 Conclusion and perspectives
Bibliography

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