Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Decay estimates for the biharmonic equation with applications to Saint-Venant principles in plane elasticity and Stokes flows

Author: C. O. Horgan
Journal: Quart. Appl. Math. 47 (1989), 147-157
MSC: Primary 73C02; Secondary 31A30, 35B40, 73C10, 76D05
DOI: https://doi.org/10.1090/qam/987903
MathSciNet review: 987903
Full-text PDF

References | Similar Articles | Additional Information

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

  • [1] James K. Knowles, An energy estimate for the biharmonic equation and its application to Saint-Venant’s principle in plane elastostatics, Indian J. Pure Appl. Math. 14 (1983), no. 7, 791–805. MR 714832
  • [2] Cornelius O. Horgan and James K. Knowles, Recent developments concerning Saint-Venant’s principle, Adv. in Appl. Mech. 23 (1983), 179–269. MR 889288
  • [3] M. E. Gurtin, The linear theory of elasticity, Handbuch der Physik, S. Flügge and C. Truesdell (eds.), Vol. 6a/2, Springer-Verlag, Berlin, 1972, pp. 1-295
  • [4] C. O. Horgan, Plane entry flows and energy estimates for the Navier-Stokes equations, Arch. Rational Mech. Anal. 68 (1978), no. 4, 359–381. MR 0521600, https://doi.org/10.1007/BF00250987
  • [5] James K. Knowles, On Saint-Venant’s principle in the two-dimensional linear theory of elasticity, Arch. Rational Mech. Anal. 21 (1966), 1–22. MR 0187480, https://doi.org/10.1007/BF00253046
  • [6] R. A. Toupin, Saint-Venant’s principle, Arch. Rational Mech. Anal. 18 (1965), 83–96. MR 0172506, https://doi.org/10.1007/BF00282253
  • [7] J. N. Flavin, On Knowles’ version of Saint-Venant’s principle in two-dimensional elastostatics, Arch. Rational Mech. Anal. 53 (1973/74), 366–375. MR 0337090, https://doi.org/10.1007/BF00281492
  • [8] O. A. Oleĭnik and G. A. Iosif′jan, The Saint-Venant principle in plane elasticity theory, Dokl. Akad. Nauk SSSR 239 (1978), no. 3, 530–533 (Russian). MR 0502616
  • [9] O. A. Oleinik and G. A. Yosifian, The Saint-Venant principle in the two-dimensional theory of elasticity and boundary problems for a biharmonic equation in unbounded domains, Sibirsk. Mat. Zh. 19, 1154-1165 (1978) (translated in Siberian Math. J. 19, 813-822 (1978))
  • [10] O. A. Oleĭnik, Energetic estimates analogous to the Saint-Venant principle and their applications, Equadiff IV (Proc. Czechoslovak Conf. Differential Equations and their Applications, Prague, 1977) Lecture Notes in Math., vol. 703, Springer, Berlin, 1979, pp. 328–339. MR 535353
  • [11] O. A. Oleinik, Applications of the energy estimates analogous to Saint-Venant's principle to problems of elasticity and hydrodynamics, Lecture Notes in Phys. 90, 422-432 (1979)
  • [12] J. L. Ericksen, Special topics in elastostatics, Advances in Applied Mechanics, C. S. Yih (ed.), Vol. 17, Academic Press, New York, 1977, pp. 189-244
  • [13] R. G. Muncaster, Saint-Venant’s problem in nonlinear elasticity: a study of cross sections, Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, Res. Notes in Math., vol. 39, Pitman, Boston, Mass.-London, 1979, pp. 17–75. MR 584396
  • [14] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge University Press, Cambridge, 1967
  • [15] S. G. Mikhlin, Variational methods in mathematical physics, Translated by T. Boddington; editorial introduction by L. I. G. Chambers. A Pergamon Press Book, The Macmillan Co., New York, 1964. MR 0172493
  • [16] Cornelius O. Horgan, A note on a class of integral inequalities, Proc. Cambridge Philos. Soc. 74 (1973), 127–131. MR 0331152
  • [17] J. N. Flavin and R. J. Knops, Some convexity considerations for a two-dimensional traction problem, Z. Angew. Math. Phys. 39 (1988), no. 2, 166–176. MR 937701, https://doi.org/10.1007/BF00945763
  • [18] P. Vafeades and C. O. Horgan, Exponential decay estimates for solutions of the von Kármán equations on a semi-infinite strip, Arch. Rational Mech. Anal. 104 (1988), no. 1, 1–25. MR 956565, https://doi.org/10.1007/BF00256930

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73C02, 31A30, 35B40, 73C10, 76D05

Retrieve articles in all journals with MSC: 73C02, 31A30, 35B40, 73C10, 76D05

Additional Information

DOI: https://doi.org/10.1090/qam/987903
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society