Inverse Laplace Transforms Encountered in Hyperbolic Problems of Non-Stationary Fluid-Structure Interaction

Iakovlev, Serguei

Canadian mathematical bulletin, Tome 50 (2007) no. 4, pp. 547-566

Résumé

The paper offers a study of the inverse Laplace transforms of the functions ${{I}_{n}}\left( rs \right)\,{{\{sI_{n}^{\prime }\,\left( s \right)\}}^{-1}}$ where ${{I}_{n}}$ is the modified Bessel function of the first kind and $r$ is a parameter. The present study is a continuation of the author's previous work on the singular behavior of the special case of the functions in question, $r=1$ . The general case of $r\,\in \,\left[ 0,\,1 \right]$ is addressed, and it is shown that the inverse Laplace transforms for such $r$ exhibit significantly more complex behavior than their predecessors, even though they still only have two different types of points of discontinuity: singularities and finite discontinuities. The functions studied originate from non-stationary fluid-structure interaction, and as such are of interest to researchers working in the area.

Détail

DOI : 10.4153/CMB-2007-053-1

Mots-clés : 44A10, 44A20, 33C10, 40A30, 74F10, 76Q05

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