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 Free Access
References |
Similar Articles |
Additional Information
- 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
- Cornelius O. Horgan and James K. Knowles, Recent developments concerning Saint-Venant’s principle, Adv. in Appl. Mech. 23 (1983), 179–269. MR 889288
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
- 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 521600, DOI https://doi.org/10.1007/BF00250987
- 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 187480, DOI https://doi.org/10.1007/BF00253046
- R. A. Toupin, Saint-Venant’s principle, Arch. Rational Mech. Anal. 18 (1965), 83–96. MR 172506, DOI https://doi.org/10.1007/BF00282253
- 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 337090, DOI https://doi.org/10.1007/BF00281492
- 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
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))
- 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
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)
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
- 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
G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge University Press, Cambridge, 1967
- S. G. Mikhlin, Variational methods in mathematical physics, The Macmillan Co., New York, 1964. Translated by T. Boddington; editorial introduction by L. I. G. Chambers; A Pergamon Press Book. MR 0172493
- Cornelius O. Horgan, A note on a class of integral inequalities, Proc. Cambridge Philos. Soc. 74 (1973), 127–131. MR 331152, DOI https://doi.org/10.1017/s0305004100047873
- 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, DOI https://doi.org/10.1007/BF00945763
- 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, DOI https://doi.org/10.1007/BF00256930
J. 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, 791–805 (1983)
C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant’s principle, in Advances in Applied Mechanics, T. Y. Wu and J. W. Hutchinson (eds.), Vol. 23, Academic Press, San Diego, 1983, pp. 179–269
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
C. O. Horgan, Plane entry flows and energy estimates for the Navier–Stokes equations, Arch. Rat. Mech. Anal. 68, 359–381 (1978)
J. K. Knowles, On Saint-Venant’s principle in the two-dimensional linear theory of elasticity, Arch. Rat. Mech. Anal. 21, 1–22 (1966)
R. A. Toupin, Saint-Venant’s principle, Arch. Rat. Mech. Anal. 18, 83–96 (1965)
J. N. Flavin, On Knowles’ version of Saint-Venant’s principle in two-dimensional elastostatics, Arch. Rat. Mech. Anal. 53, 366–375 (1974)
O. A. Oleinik and G. A. Yosifian, On Saint-Venant’s principle in plane elasticity theory, Dokl. Akad. Nauk. SSSR 239, 530–533 (1978) (translated in Soviet Math. Dokl. 19, 364–368 (1978))
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))
O. A. Oleinik, Energetic estimates analogous to the Saint-Venant principle and their applications, Equadiff IV, J. Fabera (ed.), Lecture Notes in Math. 703, 328–339 (1979)
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)
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
R. G. Muncaster, Saint-Venant’s problem in nonlinear elasticity: a study of cross-sections, in Nonlinear Analysis and Mechanics: Heriot Watt Symposium, R. J. Knops (ed.), Vol. IV, Pitman, London, 1979, pp. 17–75
G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge University Press, Cambridge, 1967
S. G. Mikhlin, Variational methods in mathematical physics, Macmillan, New York, 1964
C. O. Horgan, A note on a class of integral inequalities, Proc. Cambridge Philos. Soc. 74, 127–131 (1973)
J. N. Flavin and R. J. Knops, Some convexity considerations for a two-dimensional traction problem, J. of Appl. Math. and Phys. (ZAMP) 39, 166–176 (1988)
P. Vafeades and C. O. Horgan, Exponential decay estimates for solutions of the von Kármán equations on a semi-infinite strip, Arch. Rat. Mech. Anal. 104, 1–25 (1988)
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
Article copyright:
© Copyright 1989
American Mathematical Society