Symmetry and scaling properties of the von Kármán equations

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 49, Issue 5, 1998, Pages 710-729

  Chien, C S ^a   Kuo, Y J ^a   Mei, Z ^b  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

^b PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

Bifurcations; Central difference approximations; Scaling laws; Symmetries; Von K rm n equations

Indexed keywords

EID: 0032342822     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001487     Document Type: Article

References (20)

1. E.L. Allgower, K. Böhrner and Z. Mei, On a problem decomposition for semi-linear nearly symmetric elliptic problems. In: Parallel Algorithms for PDEs, W. Hackbusch (Ed.), Vieweg Verlag, 1991, 1-17.
2. E.L. Allgower, K. Böhmer and Z. Mei, Branch switching at a corank-4 bifurcation point of semi-linear elliptic problems with symmetry, IMA J. Numer. Anal. 14 (1994), 161-182.
3. E.L. Allgower and K. Georg. Numerical Continuation: An Introduction, Springer-Verlag, Berlin 1990.
4. S. S. Antman, Nonlinear Problems of Elasticity, Springer-Verlag, New York 1995.
5. P.J. Aston, Analysis and computation of symmetry-breaking bifurcation and scaling laws using group theoretic methods, SIAM J. Math. Anal., 22 (1991), 181-212.
6. A. Bossavit, Symmetry, group, and boundary value problems. A progressive introduction to noncommutative harmonic analysis of partial differential equations in domains with geometrical symmetry, Comput. Meths in Appl. Mech. Engrg. 56 (1986), 167-215.
7. C.-S. Chien and M.-S. Chen, Multiple bifurcation in the von Kármán equations, SIAM J. Sci. Comput., 18 (1997), to appear.
8. C.-S. Chien, S.-Y. Gong and Z. Mei, Mode jumping in the von Kármán equations, SIAM J. Sci. Comput., to appear.
9. C.-S Chien, W.-W. Lin and Z. Mei, Exploiting Symmetry for Semilinear Elliptic problems, Tech. Report NSC 87-2115-M-005-005.
10. P.G. Ciarlet, A justification of the von Kármán equations, Arch. Rational Mech. Anal. 73 (1980), 349-389.
11. J.D. Crawford, Normal forms for driven surface waves, Physica D, 52 (1991), 429-457.
12. J.D. Crawford, M. Golubitsky, E. Knobloch, M.G.M. Gomes and I.N. Stewart, Boundary conditions as symmetry constraints, In: Singularity Theory and its Applications, Lecture Notes in Math. 1463, Springer, New York 1991, 1-39.
13. M. Golubitsky, J. Stewart and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. II, Springer-Verlag, New York 1988.
14. M.G.M. Gomes and I.N. Stewart, Steady PDEs on generalized rectangles: a change of genericity in mode interactions, Nonlinearity 7 (1994), 253-272.
15. T.J. Healey and H. Kielhöfer, Symmetry and nodal properties in global bifurcation analysis of quasi-linear elliptic equations. Arch. Rational Mech. Anal., 113 (1991), 299-311.
16. E.J. Holder and D.G. Schaeffer, Boundary conditions and mode jumping in the von Kármán equations SIAM J. Math. Anal., J. 15 (1984), 446-458.
17. Z. Mei, Utilization of scaling laws and symmetries in the path following of a semilinear elliptic problem. In: E.L. Allgower, K. Böhmer and M. Golubitsky (Eds.), Bifurcation and Symmetry, Volume 104 of ISNM, Birkhäuser Verlag, Basel 1992, 263-273.
18. D. Schaeffer and M. Golubitsky, Boundary conditions and mode jumping in the buckling of a rectangular plate, Commun. Math. Phys., 69 (1979), 209-236.
19. M. Stein, Loads and deformations of buckled rectangular plates. NASA Tech. Rep. R-40, 1959.
20. R. Szilard, Theory and Analysis of Plates-Classical and Numerical Methods. Civil Engrg. & Engrg. Mech. Series. Prentice Hall, INC, New Jersey 1974.