Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

The completeness of Biot's solution of the coupled thermoelastic problem


Author: A. Verruijt
Journal: Quart. Appl. Math. 26 (1969), 485-490
MSC: Primary 73.35; Secondary 35.00
DOI: https://doi.org/10.1090/qam/239802
MathSciNet review: 239802
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In one of his papers on the theory of thermoelasticity, M. A. Biot [2] has presented a solution to the differential equations very similar to the well-known Boussinesq--Papcovitch solution in the theory of elasticity. In this note it is proved that this solution is complete, the proof being based upon Mindlin's theorem of completeness of the Boussinesq--Papcovitch solution in elasticity.


References [Enhancements On Off] (What's this?)

  • [1] O. D. Kellogg, Foundations of potential theory, Springer, Berlin, 1929 MR 0222317
  • [2] M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27, 240-253 (1956) MR 0077441
  • [3] P. F. Papcovitch, Solution générale des équations différentielles fondamentales d'élastictté, exprimé par trois fonctions harmoniques, C. R. Acad. Sci. Paris 195, 513-516 (1932)
  • [4] H. Neuber, Ein neuer Ansatz zur Lösung der Grundgleichungen der Elastizitätstheorie, Z. angew. Math. Mech. 14, 203-212 (1934)
  • [5] J. Boussinesq, Application des potentiels ä l'étude de l'équilibre et du mouvement des solides elastiques, Gauthiera-Villars, Paris, 1885
  • [6] R. D. Mindlin, Note on the Galerkin and Papkovich stress functions, Bull. Amer. Math. Soc. 42, 373-376 (1936) MR 1563303
  • [7] R. A. Eubanka and E. Sternberg, On the completeness of the Boussinesq-Papkovich stress functions, J. Rational Mech. Anal. 5, 735-746 (1956)
  • [8] H. B. Phillips, Vector analysis, Wiley, New York, 1933
  • [9] L. R. Ford, Differential equations, McGraw-Hill, New York, 1955

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73.35, 35.00

Retrieve articles in all journals with MSC: 73.35, 35.00


Additional Information

DOI: https://doi.org/10.1090/qam/239802
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society