Two-sided estimates in linear elastodynamics (Q1066704)

Methods of bounding from above and below the solutions of self-adjoint boundary value problems in linear elastostatics are already well known [see e.g. \textit{G. Rieder}, Z. Angew. Math. Mech. 52, T 340-T 347 (1972; Zbl 0248.73009)]. Our purpose here is to extent these methods to linear problems in elastodynamics. So, we present a procedure, which provides two-sided solution estimates for the mixed boundary-initial-value problem of linear elastodynamics. This procedure is based on taking Laplace transforms of the problem conditions and then using some functional analysis concepts to obtain both upper and lower bounds, either global or local, for the solution in the transform-domain. Finally, the introduction of appropriate ''weight functions'' enables one to get back to the original time-domain while preserving the bracketing character of the obtained estimates.