Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the completeness of a method of potentials in elastodynamics

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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Additional Information

Ronald Y. S. Pak
Affiliation: Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, Colorado 80309-0428
Email: pak@colorado.edu

Morteza Eskandari-Ghadi
Affiliation: Civil Engineering Department, University of Science and Technology of Mazandaran, Iran
Email: ghadi@ustmb.ac.ir

DOI: https://doi.org/10.1090/S0033-569X-07-01074-X
Keywords: Elasticity, completeness, potentials, mechanics, wave equation, vector calculus, elastodynamics, Helmholtz, solenoidal field, Laplacian
Received by editor(s): May 24, 2007
Published electronically: October 17, 2007
Dedicated: A tribute to Eli Sternberg
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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