Geodesic
Inverse Laplace Transforms Encountered in Hyperbolic Problems of Non-Stationary Fluid-Structure Interaction
Canadian mathematical bulletin, Tome 50 (2007) no. 4, pp. 547-566

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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.
DOI : 10.4153/CMB-2007-053-1
Mots-clés : 44A10, 44A20, 33C10, 40A30, 74F10, 76Q05 
Iakovlev, Serguei. Inverse Laplace Transforms Encountered in Hyperbolic Problems of Non-Stationary Fluid-Structure Interaction. Canadian mathematical bulletin, Tome 50 (2007) no. 4, pp. 547-566. doi: 10.4153/CMB-2007-053-1
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     author = {Iakovlev, Serguei},
     title = {Inverse {Laplace} {Transforms} {Encountered} in {Hyperbolic} {Problems} of {Non-Stationary} {Fluid-Structure} {Interaction}},
     journal = {Canadian mathematical bulletin},
     pages = {547--566},
     year = {2007},
     volume = {50},
     number = {4},
     doi = {10.4153/CMB-2007-053-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-053-1/}
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