Abstract
In this chapter we study the wave equation
on an open subset Ω of ℝn. We will use the theory of cosine functions and work on L 2 (Ω). We first consider the Laplacian with Dirichlet boundary conditions. This is a selfadjoint operator and well-posedness is a consequence of the spectral theorem. A further aim is to replace the Laplace operator by a general elliptic operator. This will be done by a perturbation theorem for selfadjoint operators which we prove in Section 7.1.
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© 2001 Springer Basel AG
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Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F. (2001). The Wave Equation. In: Vector-valued Laplace Transforms and Cauchy Problems. Monographs in Mathematics, vol 96. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5075-9_7
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DOI: https://doi.org/10.1007/978-3-0348-5075-9_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5077-3
Online ISBN: 978-3-0348-5075-9
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