Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T16:57:31.027Z Has data issue: false hasContentIssue false

Hölder continuous dependence in nonlinear elastodynamics

Published online by Cambridge University Press:  14 November 2011

Stan Chiriţă
Affiliation:
Mathematical Seminarium, University of Iaşi, 6600-Iaşi, Romania

Synopsis

In this paper we establish conditions to prove that if classical solutions to the initial boundary value problems for nonlinear elastodynamics exist, then they depend Hölder continuously on their initialdata and body forces.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1986

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

1Dafermos, C. M.. The second law of thermodynamics and stability. Arch. Rational Mech. Anal. 70 (1979), 167179.CrossRefGoogle Scholar
2Knops, R. J. and Payne, L. E.. Some uniqueness and continuous dependence theorems for nonlinear elastodynamics in exterior domains. Applicable Anal. 5 (1983), 3351.CrossRefGoogle Scholar
3Knops, R. J. and Payne, L. E.. Uniqueness and continuous dependence of the null solution in the Cauchy problem for a nonlinear elliptic system. Mathematical Research—Inverse and Improperly Posed Problems in Differential Equations (ed. Anger, G.) 1, 151160 (Berlin: Akademie Verlag, 1979).CrossRefGoogle Scholar
4Fichera, G.. Existence theorems in elasticity. In Encyclopedia of Physics, Truesdell, C. (ed.), Vla/2, 345389 (Berlin: Springer, 1972).Google Scholar
5Gurtin, M. E. and Spector, S. J.. On stability and uniqueness in finite elasticity. Arch. Rational Mech. Anal. 70 (1979), 153165.CrossRefGoogle Scholar
6Ball, J. M.. Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63 (1977), 337403.CrossRefGoogle Scholar
7Antman, S. S.. Coercivity conditions in nonlinear elasticity. In Systems of nonlinear partial differential equations, Ball, J. M. (ed.), 289297 (Dordrecht: Reidel, 1983).CrossRefGoogle Scholar
8Brun, L. and Potier-Ferry, M.. Thermodynamique et stabilite du solide elastique. C.R. Acad. Sci. Paris 296 (1983), 401404.Google Scholar
9Corduneanu, C.. Principles of differential and integral equations (New York: Chelsea, 1977).Google Scholar
10Knops, R. J. and Payne, L. E.. On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity. Internal J. Solids and Structures 6 (1970), 11731184.CrossRefGoogle Scholar
11Truesdell, C. A. and Noll, W.. The non-linear field theories of mechanics. In Encyclopedia of Physics, Flügge, S. (ed.) III/3 (Berlin: Springer, 1965).Google Scholar
12Wheeler, L. T.. A uniqueness theorem for the displacement problem in finite elastodynamics. Arch. Rational Mech. Anal. 63 (1977), 183189.CrossRefGoogle Scholar
13Chirija, S.. Uniqueness and continuous data dependence in dynamical problems of nonlinearthermoelasticity. J. Thermal Stresses 5 (1982), 331346.CrossRefGoogle Scholar
14Knowles, J. K. and Sternberg, E.. On the failure of ellipticity of the equations for finite elastostatic plane strain. Arch. Rational Mech. Anal 63 (1977), 321336.CrossRefGoogle Scholar
15Ball, J. M.. Strict convexity, strong ellipticity, and the regularity of weak solutions to nonlinear variational problems. Math. Proc. Camb. Philos. Soc. 87 (1980), 501513.CrossRefGoogle Scholar