In this paper the regularity properties of second-order hyperbolic equations defined over a rectangular domain Θ with boundary Γ under the action of a Neumann boundary forcing term in L 2 (0, T ; H 1/4 (Γ)) are investigated. With this given boundary input, we prove by a cosine operator/functional analytical approach that not only is the solution of the wave equation and its derivatives continuous in time, with their pointwise values in a basic energy space (in the interior of Ω), but also that a trace regularity thereof can be assigned for the solution’s time derivative in an appropriate (negative) Sobolev space. This new-found information on the solution and its traces is crucial in handling a mathematical model derived for a particular fluid/structure interaction system.
Applied Mathematics and Optimization – Springer Journals
Published: Mar 1, 1997
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