On the completeness of a method of potentials in elastodynamics

Pak, Ronald; Eskandari-Ghadi, Morteza

doi:10.1090/S0033-569X-07-01074-X

Authors: Ronald Y. S. Pak and Morteza Eskandari-Ghadi
Journal: Quart. Appl. Math. 65 (2007), 789-797
MSC (2000): Primary 74B05, 35Q72; Secondary 35L05
DOI: https://doi.org/10.1090/S0033-569X-07-01074-X
Published electronically: October 17, 2007
MathSciNet review: 2370361
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Abstract: In this paper, the theoretical foundation of a compact scalar potential method in three-dimensional classical elastodynamics is substantiated. Beginning with a derivation of two basic lemmas on the decomposition and integration of wave solutions and vector fields which are apt to be of interest to general mechanics and analysis, the treatment proceeds to a proof of the completeness of the proposed representation as well as its extension to non-zero body forces.

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