Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T11:04:48.097Z Has data issue: false hasContentIssue false

On the traction problem for linear elastostatics in exterior domains

Published online by Cambridge University Press:  14 November 2011

Mariarosaria Padula
Affiliation:
Istituto di Matematica “R. Caccioppoli”, Mezzocannone 8, 80134 Naples, Italy

Synopsis

In this note, we study the well-posedness of the exterior traction value problem for linear anisotropic non-homogeneous elastostatics. We prove existence and continuous dependence upon the data. In particular, in the isotropic homogeneous case, provided the body force is “simple”, we show that solutions tend to zero uniformly at large spatial distances.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Fichera, G.. Existence theorems in elasticity. Handbuch der Physik, Bd VIa/2 (Heidelberg: Springer, 1972).Google Scholar
2Fichera, G.. II teorema del massimo modulo per le equazioni dell'elastostatica tridimensionale. Arch. Rational Mech. Anal. 7(1961), 373387.CrossRefGoogle Scholar
3Knops, R. J. and Payne, L. E.. Some uniqueness and continuous dependence theorems for nonlinear elastodynamics in exterior domains. Applicable Math. (to appear).Google Scholar
4Rizzonelli, P. Castellani. On the first boundary value problem for the classical theory of elasticity in a three-dimensional domain with a singular boundary. J. Elasticity 3 (1973), 230245.CrossRefGoogle Scholar
5Wilcox, C. H.. Uniqueness theorems for displacement fields with locally finite energy in linear elastostatics. J. Elasticity 9 (1979), 221243.CrossRefGoogle Scholar
6Galdi, G. P. and Rionero, S.. On the well-posedness of the equilibrium problem for linear elasticity in unbounded regions. J. Elasticity 10 (1980), 333340.CrossRefGoogle Scholar
7Howell, K. B.. Uniqueness in linear elastostatics for problems involving unbounded bodies. J. Elasticity 10 (1980), 407427.CrossRefGoogle Scholar
8Kufner, A. et al. Function Spaces (Leyden: Nordhoff Int. Publ., 1977).Google Scholar
9Adams, R. A.. Sobolev Spaces (London: Academic Press, 1975).Google Scholar
10Ladyzhenskaya, O. A.. The Mathematical Theory of Viscous Incompressible Flow (New York: Gordon & Breach, 1968).Google Scholar
11Freidrichs, K. O.. On the boundary value problems of the theory of elasticity and Korn's inequality. Ann. of Math. 48 (1947), 441471.CrossRefGoogle Scholar
12Gurtin, M. E.. Theory of elasticity. Handbuch der Physik, Bd VI, 2nd edn (Berlin: Springer, 1971).Google Scholar
13Fichera, G.. Linear elliptic differential systems and eigenvalue problems. Lecture Notes in Mathematics 8 (Berlin: Springer, 1965).Google Scholar
14Valent, T.. Teoremi di esistenza e unicita in elastostatica finita. Rend. Sem. Mat. Univ. Padova 60 (1979), 165181.Google Scholar
15Témam, R.. Navier-Stokes Equations. Stud. Math. Appl. (Amsterdam: North Holland, 1977).Google Scholar
16Galdi, G. P.. Variational methods for stability of fluid motions in unbounded domains. Ricerche Mat. 27 (1978), 387404.Google Scholar
17Galdi, G. P., Some properties of steady solutions to the Navier-Stokes equations in unbounded domains. Proceedings of the Symposium on “Mathematical methods in the dynamics of fluids and ionized gases”, 4564 (Trieste: University Press, 1981).Google Scholar
18Gurtin, M. E. and Sternberg, E.. Theorems in linear elastostatics for exterior domains. Arch. Rational Mech. Anal. 8 (1961), 99119.CrossRefGoogle Scholar
19Galdi, G. P.. The maximum modulus theorem for linear elasticity on exterior domains. Internal Report, University of Naples, 1981.Google Scholar
20Knops, R. J. and Payne, L. E.. Uniqueness theorems in linear elasticity. Springer Tracts in Natural Philosophy 19 (Berlin: 1971).Google Scholar