Eigenfunction Expansion Solutions of the Linear Viscoelastic Wave Equation
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Thu, 13/05/2010 12:30 |
David Al-Attar (Department of Earth Sciences, University of Oxford) |
OxPDE Lunchtime Seminar  |
Gibson 1st Floor SR |
| In this talk we discuss the solution of the elastodynamic equations in a bounded domain with hereditary-type linear viscoelastic constitutive relation. Existence, uniqueness, and regularity of solutions to this problem is demonstrated for those viscoelastic relaxation tensors satisfying the condition of being completely monotone. We then consider the non-self-adjoint and non-linear eigenvalue problem associated with the frequency-domain form of the elastodynamic equations, and show how the time-domain solution of the equations can be expressed in terms of an eigenfunction expansion. | |||